<h1>Simon, Barry</h1> <h2>Article from <a href="https://authors.library.caltech.edu">CaltechAUTHORS</a></h2> <ul> <li>Banks, Jess and Breuer, Jonathan, el al. (2024) <a href="https://authors.library.caltech.edu/records/atth2-7h963">A useful formula for periodic Jacobi matrices on trees</a>; Proceedings of the National Academy of Sciences; Vol. 121; No. 23; e2315218121; <a href="https://doi.org/10.1073/pnas.2315218121">10.1073/pnas.2315218121</a></li> <li>Simon, Barry (2022) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20220301-900160000">The strong Gauss–Lucas theorem and analyticity of correlation functions via the Lee–Yang theorem</a>; Journal of Mathematical Physics; Vol. 63; No. 3; Art. No. 033302; <a href="https://doi.org/10.1063/5.0077229">10.1063/5.0077229</a></li> <li>Simon, Barry (2022) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20220222-706506000">Twelve tales in mathematical physics: An expanded Heineman prize lecture</a>; Journal of Mathematical Physics; Vol. 63; No. 2; Art. No. 021101; <a href="https://doi.org/10.1063/5.0056008">10.1063/5.0056008</a></li> <li>Christiansen, Jacob S. and Simon, Barry, el al. (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20211129-220847957">Asymptotics of Chebyshev polynomials, V. residual polynomials</a>; Ramanujan Journal; <a href="https://doi.org/10.1007/s11139-021-00500-0">10.1007/s11139-021-00500-0</a></li> <li>Christiansen, Jacob S. and Simon, Barry, el al. (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20210423-080608586">Remarks on periodic Jacobi matrices on trees</a>; Journal of Mathematical Physics; Vol. 62; No. 4; Art. No. 042101; <a href="https://doi.org/10.1063/5.0033702">10.1063/5.0033702</a></li> <li>Christiansen, Jacob S. and Simon, Barry, el al. (2020) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20190501-093308068">Asymptotics of Chebyshev Polynomials. IV. Comments on the Complex Case</a>; Journal d'Analyse Mathématique; Vol. 141; No. 1; 207-223; <a href="https://doi.org/10.1007/s11854-020-0120-9">10.1007/s11854-020-0120-9</a></li> <li>Avni, Nir and Breuer, Jonathan, el al. (2020) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200108-134956957">Periodic Jacobi Matrices on Trees</a>; Advances in Mathematics; Vol. 370; Art. No. 107241; <a href="https://doi.org/10.1016/j.aim.2020.107241">10.1016/j.aim.2020.107241</a></li> <li>Castelvecchi, Davide and Simon, Barry (2020) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200805-100854001">The mathematician who helped to reshape physics</a>; Nature; Vol. 584; No. 7819; 20-20; <a href="https://doi.org/10.1038/d41586-020-02297-2">10.1038/d41586-020-02297-2</a></li> <li>Frank, Rupert L. and Merz, Konstantin, el al. (2020) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200109-110319953">Proof of the Strong Scott Conjecture for Chandrasekhar Atoms</a>; Pure and Applied Functional Analysis; Vol. 5; No. 6; 1319-1356; <a href="https://doi.org/10.48550/arXiv.1907.04894">10.48550/arXiv.1907.04894</a></li> <li>Jitomirskaya, Svetlana and Molchanovsimon, Stanislav, el al. (2019) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200108-134330154">Alexander Gordon</a>; Journal of Spectral Theory; Vol. 9; No. 4; 1157-1164; <a href="https://doi.org/10.4171/JST/293">10.4171/JST/293</a></li> <li>Martínez–Finkelshtein, Andrei and Simanek, Brian, el al. (2019) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20190430-104322593">Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators</a>; Advances in Mathematics; Vol. 349; 992-1035; <a href="https://doi.org/10.1016/j.aim.2019.04.027">10.1016/j.aim.2019.04.027</a></li> <li>Simon, Barry (2019) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180222-132115517">Tosio Kato's work on non-relativistic quantum mechanics: part 2</a>; Bulletin of Mathematical Sciences; Vol. 9; No. 1; Art. No. 1950005; <a href="https://doi.org/10.1007/s13373-018-0121-5">10.1007/s13373-018-0121-5</a></li> <li>Christiansen, Jacob S. and Simon, Barry, el al. (2019) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180807-124147489">Asymptotics of Chebyshev Polynomials, II. DCT Subsets of ℝ</a>; Duke Mathematical Journal; Vol. 168; No. 2; 325-349; <a href="https://doi.org/10.1215/00127094-2018-0045">10.1215/00127094-2018-0045</a></li> <li>Breuer, Jonathan and Simon, Barry, el al. (2018) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170509-081147843">Large Deviations and Sum Rules for Spectral Theory - A Pedagogical Approach</a>; Journal of Spectral Theory; Vol. 8; No. 4; 1551-1581; <a href="https://doi.org/10.4171/JST/235">10.4171/JST/235</a></li> <li>Breuer, Jonathan and Simon, Barry, el al. (2018) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170509-082734416">Large Deviations and the Lukic Conjecture</a>; Duke Mathematical Journal; Vol. 167; No. 15; 2857-2902; <a href="https://doi.org/10.1215/00127094-2018-0027">10.1215/00127094-2018-0027</a></li> <li>Simon, Barry (2018) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180222-133447211">Tosio Kato's work on non-relativistic quantum mechanics: part 1</a>; Bulletin of Mathematical Sciences; Vol. 8; No. 1; 121-232; <a href="https://doi.org/10.1007/s13373-018-0118-0">10.1007/s13373-018-0118-0</a></li> <li>Simon, Barry (2018) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20190610-130435055">Tosio Kato's Work on Non-Relativistic Quantum Mechanics: A Brief Report</a>; IAMP News Bulletin; 6-25</li> <li>Böttcher, Albrecht and Simon, Barry, el al. (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20171121-100155399">Similarity Between Two Projections</a>; Integral Equations and Operator Theory; Vol. 89; No. 4; 507-518; <a href="https://doi.org/10.1007/s00020-017-2414-6">10.1007/s00020-017-2414-6</a></li> <li>Frank, Rupert L. and Simon, Barry (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587">Eigenvalue bounds for Schrödinger operators with complex potentials. II</a>; Journal of Spectral Theory; Vol. 7; No. 3; 633-658; <a href="https://doi.org/10.4171/JST/173">10.4171/JST/173</a></li> <li>Simon, Barry (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170509-073922440">Unitaries permuting two orthogonal projections</a>; Linear Algebra and its Applications; Vol. 528; 436-441; <a href="https://doi.org/10.1016/j.laa.2017.03.026">10.1016/j.laa.2017.03.026</a></li> <li>Simon, Barry (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170512-073744838">Ratio asymptotics and weak asymptotic measures for orthogonal polynomials on the real line</a>; Journal of Approximation Theory; Vol. 126; No. 2; 198-217; <a href="https://doi.org/10.1016/j.jat.2003.12.002">10.1016/j.jat.2003.12.002</a></li> <li>Christiansen, Jacob S. and Simon, Barry, el al. (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20161109-142515049">Asymptotics of Chebyshev polynomials, I: subsets of ℝ</a>; Inventiones Mathematicae; Vol. 208; No. 1; 217-245; <a href="https://doi.org/10.1007/s00222-016-0689-x">10.1007/s00222-016-0689-x</a></li> <li>Frank, Rupert L. and Lemm, Marius, el al. (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170428-160716872">Condensation of fermion pairs in a domain</a>; Calculus of Variations and Partial Differential Equations; Vol. 56; Art. No. 54; <a href="https://doi.org/10.1007/s00526-017-1140-x">10.1007/s00526-017-1140-x</a></li> <li>Krüger, Helge and Simon, Barry (2015) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20150326-081223615">Cantor polynomials and some related classes of OPRL</a>; Journal of Approximation Theory; Vol. 191; 71-93; <a href="https://doi.org/10.1016/j.jat.2014.04.003">10.1016/j.jat.2014.04.003</a></li> <li>Breuer, Jonathan and Last, Yoram, el al. (2014) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20140814-112606518">Stability of Asymptotics of Christoffel–Darboux Kernels</a>; Communications in Mathematical Physics; Vol. 330; No. 3; 1155-1178; <a href="https://doi.org/10.1007/s00220-014-1913-4">10.1007/s00220-014-1913-4</a></li> <li>Christiansen, Jacob S. and Simon, Barry, el al. (2012) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20120319-093342145">Finite Gap Jacobi Matrices, III. Beyond the Szegő Class</a>; Constructive Approximation; Vol. 35; No. 2; 259-272; <a href="https://doi.org/10.1007/s00365-012-9152-4">10.1007/s00365-012-9152-4</a></li> <li>Christiansen, Jacob S. and Simon, Barry, el al. (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20110414-085411774">Finite Gap Jacobi Matrices, II. The Szegő Class</a>; Constructive Approximation; Vol. 33; No. 3; 365-403; <a href="https://doi.org/10.1007/s00365-010-9094-7">10.1007/s00365-010-9094-7</a></li> <li>Martínez-Finkelshtein, Andrei and Simon, Barry (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20110610-081439616">Asymptotics of the L^2 norm of derivatives of OPUC</a>; Journal of Approximation Theory; Vol. 163; No. 6; 747-778; <a href="https://doi.org/10.1016/j.jat.2010.09.002">10.1016/j.jat.2010.09.002</a></li> <li>Frank, Rupert L. and Simon, Barry (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20110502-112300651">Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices</a>; Duke Mathematical Journal; Vol. 157; No. 3; 461-493; <a href="https://doi.org/10.1215/00127094-1272912">10.1215/00127094-1272912</a></li> <li>Breuer, Jonathan and Simon, Barry (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20110328-100710731">Natural boundaries and spectral theory</a>; Advances in Mathematics; Vol. 226; No. 6; 4902-4920; <a href="https://doi.org/10.1016/j.aim.2010.12.019">10.1016/j.aim.2010.12.019</a></li> <li>Simon, Barry (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20111219-134707644">On the Removal of Finite Discrete Spectrum by Coefficient Stripping</a>; Journal of Spectral Theory; Vol. 1; No. 1; 81-85; <a href="https://doi.org/10.4171/JST/3">10.4171/JST/3</a></li> <li>Breuer, Jonathan and Last, Yoram, el al. (2010) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20100830-143634133">The Nevai Condition</a>; Constructive Approximation; Vol. 32; No. 2; 221-254; <a href="https://doi.org/10.1007/s00365-009-9055-1">10.1007/s00365-009-9055-1</a></li> <li>Christiansen, Jacob S. and Simon, Barry, el al. (2010) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20100713-080234381">Finite Gap Jacobi Matrices, I. The Isospectral Torus</a>; Constructive Approximation; Vol. 32; No. 1; 1-65; <a href="https://doi.org/10.1007/s00365-009-9057-z">10.1007/s00365-009-9057-z</a></li> <li>Poltoratski, Alexei and Simon, Barry, el al. (2010) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20110201-094527717">The Hilbert transform of a measure</a>; Journal d'Analyse Mathématique; Vol. 111; No. 1; 247-265; <a href="https://doi.org/10.1007/s11854-010-0017-0">10.1007/s11854-010-0017-0</a></li> <li>Damanik, David and Killip, Rowan, el al. (2010) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20100803-145828608">Perturbations of orthogonal polynomials with periodic recursion coefficients</a>; Annals of Mathematics; Vol. 171; No. 3; 1931-2010; <a href="https://doi.org/10.4007/annals.2010.171.1931">10.4007/annals.2010.171.1931</a></li> <li>Breuer, Jonathan and Ryckman, Eric, el al. (2010) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20100301-083137497">Equality of the Spectral and Dynamical Definitions of Reflection</a>; Communications in Mathematical Physics; Vol. 295; No. 2; 531-550; <a href="https://doi.org/10.1007/s00220-009-0945-7">10.1007/s00220-009-0945-7</a></li> <li>Avila, Artur and Last, Yoram, el al. (2010) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20100928-144330506">Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum</a>; Analysis & PDE; Vol. 3; No. 1; 81-108; <a href="https://doi.org/10.2140/apde.2010.3.81">10.2140/apde.2010.3.81</a></li> <li>Christiansen, Jacob S. and Simon, Barry, el al. (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20091130-115048841">Finite gap Jacobi matrices: An announcement</a>; Journal of Computational and Applied Mathematics; Vol. 233; No. 3; 652-662; <a href="https://doi.org/10.1016/j.cam.2009.02.081">10.1016/j.cam.2009.02.081</a></li> <li>Cantero, María José and Simon, Barry (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20090728-075326318">Poisson brackets of orthogonal polynomials</a>; Journal of Approximation Theory; Vol. 158; No. 1; 3-48; <a href="https://doi.org/10.1016/j.jat.2007.07.001">10.1016/j.jat.2007.07.001</a></li> <li>Kreimer, Yury and Last, Yoram, el al. (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20090903-110552245">Monotone Jacobi parameters and non-Szegő weights</a>; Journal of Approximation Theory; Vol. 157; No. 2; 144-171; <a href="https://doi.org/10.1016/j.jat.2008.04.020">10.1016/j.jat.2008.04.020</a></li> <li>Simon, Barry (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20090708-105847182">A Celebration of Jürg and Tom</a>; Journal of Statistical Physics; Vol. 134; No. 5-6; 809-812; <a href="https://doi.org/10.1007/s10955-008-9627-7">10.1007/s10955-008-9627-7</a></li> <li>Simon, Barry (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:SIMdmj09">Weak convergence of CD kernels and applications</a>; Duke Mathematical Journal; Vol. 146; No. 2; 305-330; <a href="https://doi.org/10.1215/00127094-2008-067">10.1215/00127094-2008-067</a></li> <li>Simon, Barry (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20090918-112109981">Regularity and the Cesàro–Nevai class</a>; Journal of Approximation Theory; Vol. 156; No. 2; 142-153; <a href="https://doi.org/10.1016/j.jat.2008.04.016">10.1016/j.jat.2008.04.016</a></li> <li>Simon, Barry (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180813-091037545">Weak convergence of CD kernels and applications</a>; Duke Mathematical Journal; Vol. 146; No. 2; 305-330; <a href="https://doi.org/10.1215/00127094-2008-067">10.1215/00127094-2008-067</a></li> <li>Simon, Barry (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20100617-144018858">Schrödinger operators with purely discrete spectrum</a>; Methods of Functional Analysis and Topology; Vol. 15; No. 1; 61-66</li> <li>Killip, Rowan and Simon, Barry (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20100108-193514874">Sum rules and spectral measures of Schrödinger operators with L^2 potentials</a>; Annals of Mathematics; Vol. 170; No. 2; 739-782; <a href="https://doi.org/10.48550/arXiv.0608767">10.48550/arXiv.0608767</a></li> <li>Simon, Barry (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:SIMjam08">Two extensions of Lubinsky's universality theorem</a>; Journal d'Analyse Mathématique; Vol. 105; No. 1; 345-362; <a href="https://doi.org/10.1007/s11854-008-0039-z">10.1007/s11854-008-0039-z</a></li> <li>Frank, Rupert L. and Simon, Barry, el al. (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170408-144423477">Eigenvalue Bounds for Perturbations of Schrödinger Operators and Jacobi Matrices With Regular Ground States</a>; Communications in Mathematical Physics; Vol. 282; No. 1; 199-208; <a href="https://doi.org/10.1007/s00220-008-0453-1">10.1007/s00220-008-0453-1</a></li> <li>Hundertmark, Dirk and Simon, Barry (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20091014-110720129">Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices</a>; Journal of Mathematical Analysis and Applictions; Vol. 340; No. 2; 892-900; <a href="https://doi.org/10.1016/j.jmaa.2007.08.059">10.1016/j.jmaa.2007.08.059</a></li> <li>Last, Yoram and Simon, Barry (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20091016-144551584">Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior</a>; Communications on Pure and Applied Mathematics; Vol. 61; No. 4; 486-538; <a href="https://doi.org/10.1002/cpa.20185">10.1002/cpa.20185</a></li> <li>Damanik, David and Pushnitski, Alexander, el al. (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200716-153633045">The Analytic Theory of Matrix Orthogonal Polynomials</a>; Surveys in Approximation Theory; Vol. 4; 1-85; <a href="https://doi.org/10.48550/arXiv.0711.2703">10.48550/arXiv.0711.2703</a></li> <li>Geszetsy, Fritz and Pushnitski, Alexander, el al. (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:GESjmpag08">On the Koplienko Spectral Shift Function. I. Basics</a>; Journal of Mathematical Physics, Analysis and Geometry; Vol. 4; No. 1; 63-107; <a href="https://doi.org/10.48550/arXiv.0705.3629">10.48550/arXiv.0705.3629</a></li> <li>Simon, Barry (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20100211-153106376">CMV matrices: Five years after</a>; Journal of Computational and Applied Mathematics; Vol. 208; No. 1; 120-154; <a href="https://doi.org/10.1016/j.cam.2006.10.033">10.1016/j.cam.2006.10.033</a></li> <li>Simon, B. (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170809-102314012">Meromorphic Jost functions and asymptotic expansions for Jacobi parameters</a>; Functional Analysis and its Applications; Vol. 41; No. 2; 143-153; <a href="https://doi.org/10.1007/s10688-007-0013-z">10.1007/s10688-007-0013-z</a></li> <li>Simon, Barry (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170510-141814909">Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle</a>; Journal of Mathematical Analysis and Applictions; Vol. 329; No. 1; 376-382; <a href="https://doi.org/10.1016/j.jmaa.2006.06.076">10.1016/j.jmaa.2006.06.076</a></li> <li>Simon, Barry (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170726-115725562">Zeros of OPUC and long time asymptotics of Schur and related flows</a>; Inverse Problems and Imaging; Vol. 1; No. 1; 189-215; <a href="https://doi.org/10.3934/ipi.2007.1.189">10.3934/ipi.2007.1.189</a></li> <li>Last, Yoram and Simon, Barry (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170726-123106726">The Essential Spectrum of Schrödinger, Jacobi, and CMV Operators</a>; Journal d'Analyse Mathématique; Vol. 98; No. 1; 183-220; <a href="https://doi.org/10.1007/BF02790275">10.1007/BF02790275</a></li> <li>Davies, E. B. and Simon, B. (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170512-073744225">Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle</a>; Journal of Approximation Theory; Vol. 141; No. 2; 189-213; <a href="https://doi.org/10.1016/j.jat.2006.03.006">10.1016/j.jat.2006.03.006</a></li> <li>Damanik, David and Simon, Barry (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170725-145819291">Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegő asymptotics</a>; Inventiones Mathematicae; Vol. 165; No. 1; 1-50; <a href="https://doi.org/10.1007/s00222-005-0485-5">10.1007/s00222-005-0485-5</a></li> <li>Simon, Barry (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170711-080502782">Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficients</a>; Communications on Pure and Applied Mathematics; Vol. 59; No. 7; 1042-1062; <a href="https://doi.org/10.1002/cpa.20106">10.1002/cpa.20106</a></li> <li>Damanik, D. and Simon, B. (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170711-081744987">Jost functions and Jost solutions for Jacobi matrices, II. Decay and analyticity</a>; International Mathematics Research Notices; Vol. 2006; Art. No. 19396; <a href="https://doi.org/10.1155/IMRN/2006/19396">10.1155/IMRN/2006/19396</a></li> <li>Simon, Barry (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170726-134636444">Aizenman's Theorem for Orthogonal Polynomials on the Unit Circle</a>; Constructive Approximation; Vol. 23; No. 2; 229-240; <a href="https://doi.org/10.1007/s00365-005-0599-4">10.1007/s00365-005-0599-4</a></li> <li>Simon, Barry (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:SIMetna06">Fine structure of the zeros of orthogonal polynomials, I. A tale of two pictures</a>; Electronic Transactions on Numerical Analysis; Vol. 25; 328-368</li> <li>Simon, Barry and Totik, Vilmos (2005) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170408-133653793">Limits of zeros of orthogonal polynomials on the circle</a>; Mathematische Nachrichten; Vol. 278; No. 12-13; 1615-1620; <a href="https://doi.org/10.1002/mana.200410326">10.1002/mana.200410326</a></li> <li>Simon, Barry (2005) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170801-082824529">Meromorphic Szegő functions and asymptotic series for Verblunsky coefficients</a>; Acta Mathematica; Vol. 195; No. 2; 267-285; <a href="https://doi.org/10.1007/BF02588083">10.1007/BF02588083</a></li> <li>Damanik, David and Killip, Rowan, el al. (2005) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170726-130636631">Schrödinger Operators with Few Bound States</a>; Communications in Mathematical Physics; Vol. 258; No. 3; 741-750; <a href="https://doi.org/10.1007/s00220-005-1366-x">10.1007/s00220-005-1366-x</a></li> <li>Simon, Barry (2005) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170512-073745361">Fine structure of the zeros of orthogonal polynomials, II. OPUC with competing exponential decay</a>; Journal of Approximation Theory; Vol. 135; No. 1; 125-139; <a href="https://doi.org/10.1016/j.jat.2005.04.003">10.1016/j.jat.2005.04.003</a></li> <li>Simon, Barry (2005) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170510-131903213">On a theorem of Kac and Gilbert</a>; Journal of Functional Analysis; Vol. 223; No. 1; 109-115; <a href="https://doi.org/10.1016/j.jfa.2004.08.015">10.1016/j.jfa.2004.08.015</a></li> <li>Simon, Barry and Zlatoš, Andrej (2005) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170512-073745126">Higher-order Szegő theorems with two singular points</a>; Journal of Approximation Theory; Vol. 134; No. 1; 114-129; <a href="https://doi.org/10.1016/j.jat.2005.02.003">10.1016/j.jat.2005.02.003</a></li> <li>Simon, Barry (2005) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20110826-133837209">OPUC on one foot</a>; Bulletin of the American Mathematical Society; Vol. 42; No. 4; 431-460; <a href="https://doi.org/10.1090/S0273-0979-05-01075-X">10.1090/S0273-0979-05-01075-X</a></li> <li>Simon, Barry (2004) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170510-134147546">A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices</a>; Journal of Functional Analysis; Vol. 214; No. 2; 396-409; <a href="https://doi.org/10.1016/j.jfa.2003.11.006">10.1016/j.jfa.2003.11.006</a></li> <li>Gesztesy, Fritz and Simon, Barry (2004) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170801-075355675">Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schrödinger Operators</a>; Journal of Statistical Physics; Vol. 116; No. 1-4; 361-365; <a href="https://doi.org/10.1023/B:JOSS.0000037217.89500.b3">10.1023/B:JOSS.0000037217.89500.b3</a></li> <li>Simon, Barry (2004) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20110818-105014767">Orthogonal polynomials on the unit circle: New results</a>; International Mathematics Research Notices; Vol. 2004; No. 53; 2837-2880; <a href="https://doi.org/10.1155/S1073792804141664">10.1155/S1073792804141664</a></li> <li>Hundertmark, Dirk and Simon, Barry (2004) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170524-141635977">A diamagnetic inequality for semigroup differences</a>; Journal für die reine und angewandte Mathematik (Crelles Journal); Vol. 2004; No. 571; 107-130; <a href="https://doi.org/10.1515/crll.2004.036">10.1515/crll.2004.036</a></li> <li>Damanik, David and Killip, Rowan, el al. (2004) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20110920-104550878">Necessary and Sufficient Conditions in the Spectral Theory of Jacobi Matrices and Schrödinger Operators</a>; International Mathematics Research Notices; Vol. 2004; No. 22; 1087-1097; <a href="https://doi.org/10.1155/S1073792804132790">10.1155/S1073792804132790</a></li> <li>Damanik, David and Hundertmark, Dirk, el al. (2003) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170602-143616540">Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators</a>; Journal of Functional Analysis; Vol. 205; No. 2; 357-379; <a href="https://doi.org/10.1016/S0022-1236(03)00070-3">10.1016/S0022-1236(03)00070-3</a></li> <li>Simon, Barry and Zlatoš, Andrej (2003) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170515-111325638">Sum Rules and the Szegő Condition for Orthogonal Polynomials on the Real Line</a>; Communications in Mathematical Physics; Vol. 242; No. 3; 393-423; <a href="https://doi.org/10.1007/s00220-003-0906-5">10.1007/s00220-003-0906-5</a></li> <li>Killip, Rowan and Simon, Barry (2003) <a href="https://resolver.caltech.edu/CaltechAUTHORS:KILam05">Sum rules for Jacobi matrices and their applications to spectral theory</a>; Annals of Mathematics; Vol. 158; No. 1; 253-321</li> <li>Damanik, D. and Hundertmark, D., el al. (2003) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170726-131903680">Variational Estimates for Discrete Schrödinger Operators with Potentials of Indefinite Sign</a>; Communications in Mathematical Physics; Vol. 238; No. 3; 545-562; <a href="https://doi.org/10.1007/s00220-003-0868-7">10.1007/s00220-003-0868-7</a></li> <li>Kiselev, Alexander and Last, Yoram, el al. (2003) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170510-134955944">Stability of singular spectral types under decaying perturbations</a>; Journal of Functional Analysis; Vol. 198; No. 1; 1-27; <a href="https://doi.org/10.1016/S0022-1236(02)00053-8">10.1016/S0022-1236(02)00053-8</a></li> <li>Simon, Barry (2003) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20111027-081142498">The Golinskii-Ibragimov Method and a Theorem of Damanik and Killip</a>; International Mathematics Research Notices; Vol. 2003; No. 36; 1973-1986; <a href="https://doi.org/10.1155/S107379280313084X">10.1155/S107379280313084X</a></li> <li>Hundertmark, Dirk and Simon, Barry (2002) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170726-114229059">An optimal Lᵖ-bound on the Krein spectral shift function</a>; Journal d'Analyse Mathématique; Vol. 87; No. 1; 199-208; <a href="https://doi.org/10.1007/BF02868474">10.1007/BF02868474</a></li> <li>Hundertmark, Dirk and Simon, Barry (2002) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170512-073744584">Lieb–Thirring Inequalities for Jacobi Matrices</a>; Journal of Approximation Theory; Vol. 118; No. 1; 106-130; <a href="https://doi.org/10.1006/jath.2002.3704">10.1006/jath.2002.3704</a></li> <li>Kirsch, Werner and Simon, Barry (2001) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170515-105645659">Approach to equilibrium for a forced Burgers equation</a>; Journal of Evolution Equations; Vol. 1; No. 4; 411-419; <a href="https://doi.org/10.1007/PL00001380">10.1007/PL00001380</a></li> <li>Simon, Barry (2000) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170510-140505304">Resonances in One Dimension and Fredholm Determinants</a>; Journal of Functional Analysis; Vol. 178; No. 2; 396-420; <a href="https://doi.org/10.1006/jfan.2000.3669">10.1006/jfan.2000.3669</a></li> <li>Ramm, Alexander and Simon, Barry (2000) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180320-094238430">A new approach to inverse spectral theory, III. Short-range potentials</a>; Journal d'Analyse Mathématique; Vol. 80; No. 1; 319-334; <a href="https://doi.org/10.1007/BF02791540">10.1007/BF02791540</a></li> <li>Geszetsy, Fritz and Simon, Barry (2000) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20111130-133257722">A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure</a>; Annals of Mathematics; Vol. 152; No. 2; 593-643; <a href="https://doi.org/10.2307/2661393">10.2307/2661393</a></li> <li>Cordes, Heinz and Jensen, Arne, el al. (2000) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20111123-135717828">Tosio Kato (1917–1999)</a>; Notices of the American Mathematical Society; Vol. 47; No. 6; 650-657</li> <li>Simon, Barry (2000) <a href="https://resolver.caltech.edu/CaltechAUTHORS:SIMjmp00">Schrödinger operators in the twentieth century</a>; Journal of Mathematical Physics; Vol. 41; No. 6; 3523-3555; <a href="https://doi.org/10.1063/1.533321">10.1063/1.533321</a></li> <li>Gesztesy, Fritz and Simon, Barry (2000) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180511-153128441">Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum</a>; Transactions of the American Mathematical Society; Vol. 352; No. 6; 2765-2787; <a href="https://doi.org/10.1090/S0002-9947-99-02544-1">10.1090/S0002-9947-99-02544-1</a></li> <li>Gesztesy, Fritz and Simon, Barry (2000) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170801-072515055">On Local Borg–Marchenko Uniqueness Results</a>; Communications in Mathematical Physics; Vol. 211; No. 2; 273-287; <a href="https://doi.org/10.1007/s002200050812">10.1007/s002200050812</a></li> <li>Simon, Barry (1999) <a href="https://resolver.caltech.edu/CaltechAUTHORS:SIMaom99">A new approach to inverse spectral theory, I. Fundamental formalism</a>; Annals of Mathematics; Vol. 150; No. 3; 1029-1057; <a href="https://doi.org/10.2307/121061">10.2307/121061</a></li> <li>Kiselev, Alexander and Remling, Christian, el al. (1999) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170906-131540684">Effective Perturbation Methods for One-Dimensional Schrödinger Operators</a>; Journal of Differential Equations; Vol. 151; No. 2; 290-312; <a href="https://doi.org/10.1006/jdeq.1998.3514">10.1006/jdeq.1998.3514</a></li> <li>Last, Yoram and Simon, Barry (1999) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180320-104319293">Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators</a>; Inventiones Mathematicae; Vol. 135; No. 2; 329-367; <a href="https://doi.org/10.1007/s002220050288">10.1007/s002220050288</a></li> <li>Simon, Barry (1998) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170829-154200373">The Classical Moment Problem as a Self-Adjoint Finite Difference Operator</a>; Advances in Mathematics; Vol. 137; No. 1; 82-203; <a href="https://doi.org/10.1006/aima.1998.1728">10.1006/aima.1998.1728</a></li> <li>Simon, Barry (1998) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180511-153846768">Spectral averaging and the Krein spectral shift</a>; Proceedings of the American Mathematical Society; Vol. 126; No. 5; 1409-1413; <a href="https://doi.org/10.1090/S0002-9939-98-04261-0">10.1090/S0002-9939-98-04261-0</a></li> <li>Kiselev, Alexander and Last, Yoram, el al. (1998) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180320-092711915">Modified Prüfer and EFGP Transforms and the Spectral Analysis of One-Dimensional Schrödinger Operators</a>; Communications in Mathematical Physics; Vol. 194; No. 1; 1-45; <a href="https://doi.org/10.1007/s002200050346">10.1007/s002200050346</a></li> <li>Last, Yoram and Simon, Barry (1998) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170906-104652888">Modified Prüfer and EFGP Transforms and Deterministic Models with Dense Point Spectrum</a>; Journal of Functional Analysis; Vol. 154; No. 2; 513-530; <a href="https://doi.org/10.1006/jfan.1997.3192">10.1006/jfan.1997.3192</a></li> <li>del Rio, Rafael and Simon, Barry (1997) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180719-132519253">Point spectrum and mixed spectral types for rank one perturbations</a>; Proceedings of the American Mathematical Society; Vol. 125; No. 12; 3593-3599; <a href="https://doi.org/10.1090/S0002-9939-97-03997-X">10.1090/S0002-9939-97-03997-X</a></li> <li>Gesztesy, Fritz and Simon, Barry (1997) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180110-165033558">m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices</a>; Journal d'Analyse Mathématique; Vol. 73; No. 1; 267-297; <a href="https://doi.org/10.1007/BF02788147">10.1007/BF02788147</a></li> <li>del Rio, Rafael and Gesztesy, Fritz, el al. (1997) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170918-101826478">Inverse spectral analysis with partial information on the potential. III. Updating boundary conditions</a>; International Mathematics Research Notices; Vol. 1997; No. 15; 751-758; <a href="https://doi.org/10.1155/S1073792897000494">10.1155/S1073792897000494</a></li> <li>Del Rio, R. and Jitomirskaya, S., el al. (1996) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180315-134316740">Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization</a>; Journal d'Analyse Mathématique; Vol. 69; No. 1; 153-200; <a href="https://doi.org/10.1007/BF02787106">10.1007/BF02787106</a></li> <li>Gesztesy, F. and Simon, B., el al. (1996) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180315-135902699">Spectral deformations of one-dimensional Schrödinger operators</a>; Journal d'Analyse Mathématique; Vol. 70; No. 1; 267-324; <a href="https://doi.org/10.1007/BF02820446">10.1007/BF02820446</a></li> <li>Gesztesy, F. and Holden, H., el al. (1996) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170912-095106346">A Trace Formula for Multidimensional Schrödinger Operators</a>; Journal of Functional Analysis; Vol. 141; No. 2; 449-465; <a href="https://doi.org/10.1006/jfan.1996.0137">10.1006/jfan.1996.0137</a></li> <li>Simon, Barry (1996) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180511-162701951">Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators</a>; Proceedings of the American Mathematical Society; Vol. 124; No. 11; 3361-3369; <a href="https://doi.org/10.1090/S0002-9939-96-03599-X">10.1090/S0002-9939-96-03599-X</a></li> <li>Simon, Barry and Zhu, Yunfeng (1996) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170809-105308934">The Lyapunov Exponents for Schrödinger Operators with Slowly Oscillating Potentials</a>; Journal of Functional Analysis; Vol. 140; No. 2; 541-556; <a href="https://doi.org/10.1006/jfan.1996.0117">10.1006/jfan.1996.0117</a></li> <li>Simon, B. and Stolz, G. (1996) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180511-161415818">Operators with singular continuous spectrum, V. Sparse potentials</a>; Proceedings of the American Mathematical Society; Vol. 124; No. 7; 2073-2080; <a href="https://doi.org/10.1090/S0002-9939-96-03465-X">10.1090/S0002-9939-96-03465-X</a></li> <li>Gesztesy, F. and Simon, B., el al. (1996) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170918-100353730">Zeros of the Wronskian and Renormalized Oscillation Theory</a>; American Journal of Mathematics; Vol. 118; No. 3; 571-594; <a href="https://doi.org/10.1353/ajm.1996.0024">10.1353/ajm.1996.0024</a></li> <li>Simon, Barry (1996) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180320-112111420">Operators with singular continuous spectrum, VI. Graph Laplacians and Laplace-Beltrami operators</a>; Proceedings of the American Mathematical Society; Vol. 124; No. 4; 1177-1183; <a href="https://doi.org/10.1090/S0002-9939-96-03245-5">10.1090/S0002-9939-96-03245-5</a></li> <li>Simon, Barry (1996) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180315-112637401">Operators with Singular Continuous Spectrum, VII. Examples with Borderline Time Decay</a>; Communications in Mathematical Physics; Vol. 176; No. 3; 713-722; <a href="https://doi.org/10.1007/BF02099257">10.1007/BF02099257</a></li> <li>Gesztesy, F. and Simon, B. (1996) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20120208-090710174">Uniqueness theorems in inverse spectral theory for one-dimensional Schrödinger operators</a>; Transactions of the American Mathematical Society; Vol. 348; No. 1; 349-373; <a href="https://doi.org/10.1090/S0002-9947-96-01525-5">10.1090/S0002-9947-96-01525-5</a></li> <li>Simon, B. (1995) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180206-140113065">L^p Norms of the Borel Transform and the Decomposition of Measures</a>; Proceedings of the American Mathematical Society; Vol. 123; No. 12; 3749-3755; <a href="https://doi.org/10.2307/2161903">10.2307/2161903</a></li> <li>Hof, A. and Knill, O., el al. (1995) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180315-130513176">Singular Continuous Spectrum for Palindromic Schrödinger Operators</a>; Communications in Mathematical Physics; Vol. 174; No. 1; 149-159; <a href="https://doi.org/10.1007/BF02099468">10.1007/BF02099468</a></li> <li>Del Rio, R. and Jitomirskaya, S., el al. (1995) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180413-113435667">What is Localization?</a>; Physical Review Letters; Vol. 75; No. 1; 117-119; <a href="https://doi.org/10.1103/PhysRevLett.75.117">10.1103/PhysRevLett.75.117</a></li> <li>Kiselev, A. and Simon, B. (1995) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170906-141427255">Rank One Perturbations with Infinitesimal Coupling</a>; Journal of Functional Analysis; Vol. 130; No. 2; 345-356; <a href="https://doi.org/10.1006/jfan.1995.1074">10.1006/jfan.1995.1074</a></li> <li>Gesztesy, F. and Holden, H., el al. (1995) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180315-131739823">Absolute Summability of the Trace Relation for Certain Schrödinger Operators</a>; Communications in Mathematical Physics; Vol. 168; No. 1; 137-161; <a href="https://doi.org/10.1007/BF02099586">10.1007/BF02099586</a></li> <li>Gesztesy, F. and Simon, B. (1995) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170906-143042594">Rank One Perturbations at Infinite Coupling</a>; Journal of Functional Analysis; Vol. 128; No. 1; 245-252; <a href="https://doi.org/10.1006/jfan.1995.1030">10.1006/jfan.1995.1030</a></li> <li>Simon, Barry (1995) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170808-151736465">Operators with Singular Continuous Spectrum: I. General Operators</a>; Annals of Mathematics; Vol. 141; No. 1; 131-145</li> <li>Gesztesy, F. and Holden, H., el al. (1995) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170918-092925572">Higher order trace relations for Schrödinger operators</a>; Reviews in Mathematical Physics; Vol. 7; No. 6; 893-922; <a href="https://doi.org/10.1142/S0129055X95000347">10.1142/S0129055X95000347</a></li> <li>Jitomirskaya, S. and Simon, B. (1994) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20171107-095819082">Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators</a>; Communications in Mathematical Physics; Vol. 165; No. 1; 201-205; <a href="https://doi.org/10.1007/BF02099743">10.1007/BF02099743</a></li> <li>Del Rio, R. and Jitomirskaya, S., el al. (1994) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180413-112754476">Singular continuous spectrum is generic</a>; Bulletin of the American Mathematical Society; Vol. 31; No. 2; 208-212; <a href="https://doi.org/10.1090/S0273-0979-1994-00518-X">10.1090/S0273-0979-1994-00518-X</a></li> <li>Del Rio, R. and Makarov, N., el al. (1994) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20171120-161021287">Operators with singular continuous spectrum: II. Rank one operators</a>; Communications in Mathematical Physics; Vol. 165; No. 1; 59-67; <a href="https://doi.org/10.1007/BF02099737">10.1007/BF02099737</a></li> <li>Avron, J. and Seiler, R., el al. (1994) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170906-144540972">The Index of a Pair of Projections</a>; Journal of Functional Analysis; Vol. 120; No. 1; 220-237; <a href="https://doi.org/10.1006/jfan.1994.1031">10.1006/jfan.1994.1031</a></li> <li>Avron, Joseph E. and Seiler, Ruedi, el al. (1994) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20171107-101426795">Charge deficiency, charge transport and comparison of dimensions</a>; Communications in Mathematical Physics; Vol. 159; No. 2; 399-422; <a href="https://doi.org/10.1007/BF02102644">10.1007/BF02102644</a></li> <li>Simon, Barry (1994) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170918-091225249">Cyclic vectors in the Anderson model</a>; Reviews in Mathematical Physics; Vol. 6; No. 5a; 1183-1185; <a href="https://doi.org/10.1142/S0129055X94000420">10.1142/S0129055X94000420</a></li> <li>del Rio, R. and Simon, B., el al. (1994) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180719-140605491">Stability of Spectral Types for Sturm-Liouville Operators</a>; Mathematical Research Letters; Vol. 1; No. 4; 437-450; <a href="https://doi.org/10.4310/MRL.1994.v1.n4.a4">10.4310/MRL.1994.v1.n4.a4</a></li> <li>Gordon, Y. A. and Jakšić, V., el al. (1993) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180315-110824542">Spectral Properties of Random Schrödinger Operators with Unbounded Potentials</a>; Communications in Mathematical Physics; Vol. 157; No. 1; 23-50; <a href="https://doi.org/10.1007/BF02098017">10.1007/BF02098017</a></li> <li>Gesztesy, F. and Holden, H., el al. (1993) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180413-112125582">Trace formulae and inverse spectral theory for Schrödinger operators</a>; Bulletin of the American Mathematical Society; Vol. 29; No. 2; 250-256; <a href="https://doi.org/10.1090/S0273-0979-1993-00431-2">10.1090/S0273-0979-1993-00431-2</a></li> <li>Gesztesy, F. and Holden, H., el al. (1993) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180413-111511219">On the Toda and Kac-van Moerbeke systems</a>; Transactions of the American Mathematical Society; Vol. 339; No. 2; 849-868; <a href="https://doi.org/10.1090/S0002-9947-1993-1153014-1">10.1090/S0002-9947-1993-1153014-1</a></li> <li>Simon, Barry (1993) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180413-110907644">Large time behavior of the heat kernel: on a theorem of Chavel and Karp</a>; Proceedings of the American Mathematical Society; Vol. 118; No. 2; 513-514; <a href="https://doi.org/10.1090/S0002-9939-1993-1139473-4">10.1090/S0002-9939-1993-1139473-4</a></li> <li>Graf, Gian Michele and Simon, B. (1993) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170906-150023173">Asymptotic Series for the Ground State Energy of Schrödinger Operators</a>; Journal of Functional Analysis; Vol. 112; No. 2; 442-446; <a href="https://doi.org/10.1006/jfan.1993.1039">10.1006/jfan.1993.1039</a></li> <li>Gesztesy, F. and Simon, B. (1993) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20171120-095049793">A Short Proof of Zheludev's Theorem</a>; Transactions of the American Mathematical Society; Vol. 335; No. 1; 329-340</li> <li>Simon, Barry (1992) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20171120-104432614">The Weyl Transform and L^p Functions on Phase Space</a>; Proceedings of the American Mathematical Society; Vol. 116; No. 4; 1045-1047</li> <li>Simon, Barry (1992) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170905-100002232">Best constants in some operator smoothness estimates</a>; Journal of Functional Analysis; Vol. 107; No. 1; 66-71; <a href="https://doi.org/10.1016/0022-1236(92)90100-W">10.1016/0022-1236(92)90100-W</a></li> <li>Jakšić, V. and Molčanov, S., el al. (1992) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170809-113325669">Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps</a>; Journal of Functional Analysis; Vol. 106; No. 1; 59-79; <a href="https://doi.org/10.1016/0022-1236(92)90063-O">10.1016/0022-1236(92)90063-O</a></li> <li>Simon, Barry (1992) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180413-110242629">The Neumann Laplacian of a jelly roll</a>; Proceedings of the American Mathematical Society; Vol. 114; No. 3; 783-785; <a href="https://doi.org/10.1090/S0002-9939-1992-1076578-X">10.1090/S0002-9939-1992-1076578-X</a></li> <li>Davies, E. B. and Simon, B. (1992) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180314-071625612">Spectral properties of Neumann Laplacian of horns</a>; Geometric and Functional Analysis; Vol. 2; No. 1; 105-117; <a href="https://doi.org/10.1007/BF01895707">10.1007/BF01895707</a></li> <li>Gesztesy, F. and Graf, G. M., el al. (1992) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180313-152512594">The ground state energy of Schrödinger operators</a>; Communications in Mathematical Physics; Vol. 150; No. 2; 375-384</li> <li>Hempel, Rainer and Seco, Luis A., el al. (1991) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170829-073525996">The essential spectrum of Neumann Laplacians on some bounded singular domains</a>; Journal of Functional Analysis; Vol. 102; No. 2; 448-483; <a href="https://doi.org/10.1016/0022-1236(91)90130-W">10.1016/0022-1236(91)90130-W</a></li> <li>Davies, E. B. and Simon, B. (1991) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170830-081216215">L^p norms of non-critical Schrödinger semigroups</a>; Journal of Functional Analysis; Vol. 102; No. 1; 95-115; <a href="https://doi.org/10.1016/0022-1236(91)90137-T">10.1016/0022-1236(91)90137-T</a></li> <li>Gesztesy, F. and Holden, H., el al. (1991) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170810-072646814">Explicit construction of solutions of the modified Kadomtsev-Petviashvili equation</a>; Journal of Functional Analysis; Vol. 98; No. 1; 211-228; <a href="https://doi.org/10.1016/0022-1236(91)90096-N">10.1016/0022-1236(91)90096-N</a></li> <li>Gesztesy, F. and Schweiger, W., el al. (1991) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170408-144611234">Commutation methods applied to the mKdV-equation</a>; Transactions of the American Mathematical Society; Vol. 324; No. 2; 465-525; <a href="https://doi.org/10.1090/S0002-9947-1991-1029000-7">10.1090/S0002-9947-1991-1029000-7</a></li> <li>Simon, Barry (1990) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180315-132837134">Absence of Ballistic Motion</a>; Communications in Mathematical Physics; Vol. 134; No. 1; 209-212; <a href="https://doi.org/10.1007/BF02102095">10.1007/BF02102095</a></li> <li>Avron, Joseph E. and Seiler, Ruedi, el al. (1990) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180313-142926573">Quantum Hall effect and the relative index for projections</a>; Physical Review Letters; Vol. 65; No. 17; 2185-2188; <a href="https://doi.org/10.1103/PhysRevLett.65.2185">10.1103/PhysRevLett.65.2185</a></li> <li>Avron, J. and v. Mouche, P. H. M., el al. (1990) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20171107-100226114">On the measure of the spectrum for the almost Mathieu operator</a>; Communications in Mathematical Physics; Vol. 132; No. 1; 103-118; <a href="https://doi.org/10.1007/BF02278001">10.1007/BF02278001</a></li> <li>Carmona, René and Masters, Wen Chen, el al. (1990) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180521-151747020">Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions</a>; Journal of Functional Analysis; Vol. 91; No. 1; 117-142; <a href="https://doi.org/10.1016/0022-1236(90)90049-Q">10.1016/0022-1236(90)90049-Q</a></li> <li>Gesztesy, F. and Simon, Barry (1990) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160825-154251595">Constructing solutions of the mKdV-equation</a>; Journal of Functional Analysis; Vol. 89; No. 1; 53-60; <a href="https://doi.org/10.1016/0022-1236(90)90003-4">10.1016/0022-1236(90)90003-4</a></li> <li>Lieb, Elliott H. and Sigal, Israel M., el al. (1988) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20190826-124739793">Approximate neutrality of large-Z ions</a>; Communications in Mathematical Physics; Vol. 116; No. 4; 635-644; <a href="https://doi.org/10.1007/bf01224904">10.1007/bf01224904</a></li> <li>Avron, J. E. and Sadun, L., el al. (1988) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180413-164425306">Topological Invariants in Fermi Systems with Time-Reversal Invariance</a>; Physical Review Letters; Vol. 61; No. 12; 1329-1332; <a href="https://doi.org/10.1103/PhysRevLett.61.1329">10.1103/PhysRevLett.61.1329</a></li> <li>Englisch, H. and Kirsch, W., el al. (1988) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180413-164117904">Density of Surface States in Discrete Models</a>; Physical Review Letters; Vol. 61; No. 11; 1261-1262; <a href="https://doi.org/10.1103/PhysRevLett.61.1261">10.1103/PhysRevLett.61.1261</a></li> <li>Bollé, D. and Gesztesy, F., el al. (1987) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20120622-081911618">Witten index, axial anomaly, and Krein's spectral shift function in supersymmetric quantum mechanics</a>; Journal of Mathematical Physics; Vol. 28; No. 7; 1512-1525; <a href="https://doi.org/10.1063/1.527508">10.1063/1.527508</a></li> <li>Simon, Barry (1986) <a href="https://resolver.caltech.edu/CaltechAUTHORS:SIMpjm86">Schrödinger semigroups on the scale of Sobolev spaces</a>; Pacific Journal of Mathematics; Vol. 122; No. 2; 475-480</li> <li>Simon, Barry and Taylor, Michael, el al. (1985) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-104515007">Some Rigorous Results for the Anderson Model</a>; Physical Review Letters; Vol. 54; No. 14; 1589-1592; <a href="https://doi.org/10.1103/PhysRevLett.54.1589">10.1103/PhysRevLett.54.1589</a></li> <li>Simon, Barry (1985) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180720-164402687">Almost periodic Schrödinger operators IV. The Maryland model</a>; Annals of Physics; Vol. 159; No. 1; 157-183; <a href="https://doi.org/10.1016/0003-4916(85)90196-4">10.1016/0003-4916(85)90196-4</a></li> <li>Simon, Barry (1984) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180521-145200393">Semiclassical analysis of low lying elgenvalues. III. Width of the ground state band in strongly coupled solids</a>; Annals of Physics; Vol. 158; No. 2; 415-420; <a href="https://doi.org/10.1016/0003-4916(84)90125-8">10.1016/0003-4916(84)90125-8</a></li> <li>Delyon, Francois and Simon, Barry, el al. (1984) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-104514705">From Power-Localized to Extended States in a Class of One-Dimensional Disordered Systems</a>; Physical Review Letters; Vol. 52; No. 24; 2187-2189; <a href="https://doi.org/10.1103/PhysRevLett.52.2187">10.1103/PhysRevLett.52.2187</a></li> <li>Harrell, Evans M. and Corngold, Noel, el al. (1984) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180521-163704706">The mathematical theory of resonances whose widths are exponentially small, II</a>; Journal of Mathematical Analysis and Applictions; Vol. 99; No. 2; 447-457; <a href="https://doi.org/10.1016/0022-247X(84)90225-7">10.1016/0022-247X(84)90225-7</a></li> <li>Lieb, Elliott H. and Sigal, Israel M., el al. (1984) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-104514421">Asymptotic Neutrality of Large-Z Ions</a>; Physical Review Letters; Vol. 52; No. 12; 994-996; <a href="https://doi.org/10.1103/PhysRevLett.52.994">10.1103/PhysRevLett.52.994</a></li> <li>Simon, Barry (1983) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-104514087">Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase</a>; Physical Review Letters; Vol. 51; No. 24; 2167-2170; <a href="https://doi.org/10.1103/PhysRevLett.51.2167">10.1103/PhysRevLett.51.2167</a></li> <li>Avron, J. E. and Seiler, R., el al. (1983) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-104513799">Homotopy and Quantization in Condensed Matter Physics</a>; Physical Review Letters; Vol. 51; No. 1; 51-53; <a href="https://doi.org/10.1103/PhysRevLett.51.51">10.1103/PhysRevLett.51.51</a></li> <li>Avron, J. and Craig, W., el al. (1983) <a href="https://resolver.caltech.edu/CaltechAUTHORS:AVRjpa83.791">Large coupling behaviour of the Lyapunov exponent for tight binding one-dimensional random systems</a>; Journal of Physics A: Mathematical and General; Vol. 16; No. 7; L209-L211; <a href="https://doi.org/10.1088/0305-4470/16/7/002">10.1088/0305-4470/16/7/002</a></li> <li>Simon, Barry (1983) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180521-140632144">Equality of the density of states in a wide class of tight-binding Lorentzian random models</a>; Physical Review B; Vol. 27; No. 6; 3859-3860; <a href="https://doi.org/10.1103/PhysRevB.27.3859">10.1103/PhysRevB.27.3859</a></li> <li>Simon, Barry (1983) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180521-162122666">Some quantum operators with discrete spectrum but classically continuous spectrum</a>; Annals of Physics; Vol. 146; No. 1; 209-220; <a href="https://doi.org/10.1016/0003-4916(83)90057-X">10.1016/0003-4916(83)90057-X</a></li> <li>Simon, Barry (1982) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20201007-081705850">Almost periodic Schrödinger operators: A Review</a>; Advances in Applied Mathematics; Vol. 3; No. 4; 463-490; <a href="https://doi.org/10.1016/s0196-8858(82)80018-3">10.1016/s0196-8858(82)80018-3</a></li> <li>Simon, Barry (1982) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20120717-114851010">Continuity of the density of states in a magnetic field</a>; Journal of Physics A: Mathematical and General; Vol. 15; No. 9; 2981-2983; <a href="https://doi.org/10.1088/0305-4470/15/9/043">10.1088/0305-4470/15/9/043</a></li> <li>Simon, Barry (1981) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180521-152345997">Spectrum and continuum eigenfunctions of Schrödinger operators</a>; Journal of Functional Analysis; Vol. 42; No. 3; 347-355; <a href="https://doi.org/10.1016/0022-1236(81)90094-X">10.1016/0022-1236(81)90094-X</a></li> <li>Avron, Joseph and Simon, Barry (1981) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180521-145909947">The Asymptotics of the Gap in the Mathieu Equation</a>; Annals of Physics; Vol. 134; No. 1; 76-84; <a href="https://doi.org/10.1016/0003-4916(81)90005-1">10.1016/0003-4916(81)90005-1</a></li> <li>Avron, Joseph E. and Simon, Barry (1981) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-104513184">Almost Periodic Hill's Equation and the Rings of Saturn</a>; Physical Review Letters; Vol. 46; No. 17; 1166-1168; <a href="https://doi.org/10.1103/PhysRevLett.46.1166">10.1103/PhysRevLett.46.1166</a></li> <li>Simon, Barry (1981) <a href="https://resolver.caltech.edu/CaltechAUTHORS:SIMpjm81">Pointwise domination of matrices and comparison of ℐ_p norms</a>; Pacific Journal of Mathematics; Vol. 97; No. 2; 471-475</li> <li>Klaus, M. and Simon, Barry (1980) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180521-150501792">Coupling Constant Thresholds in Nonrelativistic Quantum Mechanics. I. Short-Range Two-Body Case</a>; Annals of Physics; Vol. 130; No. 2; 251-281; <a href="https://doi.org/10.1016/0003-4916(80)90338-3">10.1016/0003-4916(80)90338-3</a></li> <li>Schecter, M. and Simon, B. (1980) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180521-164135228">Unique continuation for Schrodinger operators with unbounded potentials</a>; Journal of Mathematical Analysis and Applictions; Vol. 77; No. 2; 482-492; <a href="https://doi.org/10.1016/0022-247X(80)90242-5">10.1016/0022-247X(80)90242-5</a></li> <li>Miller, Keith and Simon, Barry (1980) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-104512905">Quantum Magnetic Hamiltonians with Remarkable Spectral Properties</a>; Physical Review Letters; Vol. 44; No. 25; 1706-1707; <a href="https://doi.org/10.1103/PhysRevLett.44.1706">10.1103/PhysRevLett.44.1706</a></li> <li>Simon, Barry (1980) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-104512511">Decay of Correlations in Ferromagnets</a>; Physical Review Letters; Vol. 44; No. 8; 547-549; <a href="https://doi.org/10.1103/PhysRevLett.44.547">10.1103/PhysRevLett.44.547</a></li> <li>Enss, V. and Simon, B. (1980) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-124706801">Bounds on Total Cross Sections in Atom-Atom and Atom-Ion Collisions by Geometric Methods</a>; Physical Review Letters; Vol. 44; No. 5; 319-322; <a href="https://doi.org/10.1103/PhysRevLett.44.319">10.1103/PhysRevLett.44.319</a></li> <li>Avron, J. E. and Herbst, I. W., el al. (1979) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-154003229">Strongly bound states of hydrogen in intense magnetic field</a>; Physical Review A; Vol. 20; No. 6; 2287-2296; <a href="https://doi.org/10.1103/PhysRevA.20.2287">10.1103/PhysRevA.20.2287</a></li> <li>Benassi, L. and Grecchi, V., el al. (1979) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-154002869">Bender-Wu Formula and the Stark Effect in Hydrogen</a>; Physical Review Letters; Vol. 42; No. 11; 704-707; <a href="https://doi.org/10.1103/PhysRevLett.42.704">10.1103/PhysRevLett.42.704</a></li> <li>Herbst, I. W. and Simon, B. (1978) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-154002598">Stark Effect Revisited</a>; Physical Review Letters; Vol. 41; No. 2; 67-69; <a href="https://doi.org/10.1103/PhysRevLett.41.67">10.1103/PhysRevLett.41.67</a></li> <li>Avron, J. and Herbst, I., el al. (1977) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-154002275">Formation of Negative Ions in Magnetic Fields</a>; Physical Review Letters; Vol. 39; No. 17; 1068-1070; <a href="https://doi.org/10.1103/PhysRevLett.39.1068">10.1103/PhysRevLett.39.1068</a></li> <li>Dyson, Freeman J. and Lieb, Elliott H., el al. (1976) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-154001196">Phase Transitions in the Quantum Heisenberg Model</a>; Physical Review Letters; Vol. 37; No. 3; 120-123; <a href="https://doi.org/10.1103/PhysRevLett.37.120">10.1103/PhysRevLett.37.120</a></li> <li>Simon, Barry (1976) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-154000938">Universal Diamagnetism of Spinless Bose Systems</a>; Physical Review Letters; Vol. 36; No. 18; 1083-1084; <a href="https://doi.org/10.1103/PhysRevLett.36.1083">10.1103/PhysRevLett.36.1083</a></li> <li>Seiler, E. and Simon, B. (1975) <a href="https://resolver.caltech.edu/CaltechAUTHORS:SEIpnas75">An inequality among determinants</a>; Proceedings of the National Academy of Sciences of the United States of America; Vol. 72; No. 9; 3277-3278; PMCID PMC432972</li> <li>Lieb, Elliott H. and Simon, Barry (1973) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-154000408">Thomas-Fermi Theory Revisited</a>; Physical Review Letters; Vol. 31; No. 11; 681-683; <a href="https://doi.org/10.1103/PhysRevLett.31.681">10.1103/PhysRevLett.31.681</a></li> <li>Simon, Barry and Griffiths, Robert B. (1973) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-154000112">Griffiths-Hurst-Sherman Inequalities and a Lee-Yang Therorem for the(ϕ^4)_2 Field Theory</a>; Physical Review Letters; Vol. 30; No. 19; 931-933; <a href="https://doi.org/10.1103/PhysRevLett.30.931">10.1103/PhysRevLett.30.931</a></li> <li>Simon, Barry (1972) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-153959845">Summability Methods, the Strong Asymptotic Condition, and Unitarity in Quantum Field Theory</a>; Physical Review Letters; Vol. 28; No. 17; 1145-1146; <a href="https://doi.org/10.1103/PhysRevLett.28.1145">10.1103/PhysRevLett.28.1145</a></li> <li>Simon, Barry (1970) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-153959480">Borel Summability of the Ground-State Energy in Spatially Cutoff (ϕ^4)_2</a>; Physical Review Letters; Vol. 25; No. 22; 1583-1586; <a href="https://doi.org/10.1103/PhysRevLett.25.1583">10.1103/PhysRevLett.25.1583</a></li> <li>Simon, Barry (1970) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180417-154003485">Some Comments on the Jin-Martin Lower Bound</a>; Physical Review D; Vol. 1; No. 4; 1240-1241; <a href="https://doi.org/10.1103/PhysRevD.1.1240">10.1103/PhysRevD.1.1240</a></li> <li>Loeffel, J. J. and Martin, A., el al. (1969) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20181120-133838806">Pade approximants and the anharmonic oscillator</a>; Physics Letters B; Vol. 30; No. 9; 656-658; <a href="https://doi.org/10.1016/0370-2693(69)90087-2">10.1016/0370-2693(69)90087-2</a></li> <li>Simon, Barry (1969) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20181119-161054026">On the Growth of the Ground‐State Binding Energy with Increase in Potential Strength</a>; Journal of Mathematical Physics; Vol. 10; No. 8; 1415-1421; <a href="https://doi.org/10.1063/1.1664983">10.1063/1.1664983</a></li> <li>Simon, Barry (1969) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20181120-133838721">On the Growth of the Number of Bound States with Increase in Potential Strength</a>; Journal of Mathematical Physics; Vol. 10; No. 7; 1123-1126; <a href="https://doi.org/10.1063/1.1664948">10.1063/1.1664948</a></li> <li>Simon, B. (1969) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20181120-145801316">Convergence of regularized, renormalized perturbation series for super-renormalizable field theories</a>; Il Nuovo Cimento A Series 10; Vol. 59; No. 1; 199-214; <a href="https://doi.org/10.1007/bf02756356">10.1007/bf02756356</a></li> </ul>