Simon, Barry M.

• Simon, Barry (2022) The strong Gauss–Lucas theorem and analyticity of correlation functions via the Lee–Yang theorem; Journal of Mathematical Physics; Vol. 63; No. 3; Art. No. 033302; 10.1063/5.0077229
• Simon, Barry and van Enter, Aernout (2022) Lattice Systems; ISBN 9781118445112; Wiley StatsRef: Statistics Reference Online; Wiley: New York, NY; 1-8; 10.1002/9781118445112.stat00085.pub2
• Simon, Barry (2022) Twelve tales in mathematical physics: An expanded Heineman prize lecture; Journal of Mathematical Physics; Vol. 63; No. 2; Art. No. 021101; 10.1063/5.0056008
• Christiansen, Jacob S.; Simon, Barry; et el. (2021) Asymptotics of Chebyshev polynomials, V. residual polynomials; Ramanujan Journal; 10.1007/s11139-021-00500-0
• Christiansen, Jacob S.; Simon, Barry; et el. (2021) Remarks on periodic Jacobi matrices on trees; Journal of Mathematical Physics; Vol. 62; No. 4; Art. No. 042101; 10.1063/5.0033702
• Christiansen, Jacob S.; Simon, Barry; et el. (2020) Asymptotics of Chebyshev Polynomials. IV. Comments on the Complex Case; Journal d’Analyse Mathématique; Vol. 141; No. 1; 207-223; 10.1007/s11854-020-0120-9
• Avni, Nir; Breuer, Jonathan; et el. (2020) Periodic Jacobi Matrices on Trees; Advances in Mathematics; Vol. 370; Art. No. 107241; 10.1016/j.aim.2020.107241
• Castelvecchi, Davide and Simon, Barry (2020) The mathematician who helped to reshape physics; Nature; Vol. 584; No. 7819; 20-20; 10.1038/d41586-020-02297-2
• Christiansen, Jacob S.; Simon, Barry; et el. (2020) Asymptotics of Chebyshev Polynomials, III. Sets Saturating Szegő, Schiefermayr, and Totik–Widom Bounds; ISBN 978-3-030-31530-6; Analysis as a Tool in Mathematical Physics: In Memory of Boris Pavlov; Springer: Cham; 231-246; 10.1007/978-3-030-31531-3_15
• Kurasov, Pavel; Laptev, Ari; et el. (2020) Analysis as a Tool in Mathematical Physics: In Memory of Boris Pavlov; ISBN 978-3-030-31530-6; Analysis as a Tool in Mathematical Physics; Springer: Cham; 10.1007/978-3-030-31531-3
• Frank, Rupert L.; Merz, Konstantin; et el. (2020) Proof of the Strong Scott Conjecture for Chandrasekhar Atoms; Pure and Applied Functional Analysis; Vol. 5; No. 6; 1319-1356; 10.48550/arXiv.1907.04894
• Jitomirskaya, Svetlana; Molchanovsimon, Stanislav; et el. (2019) Alexander Gordon; Journal of Spectral Theory; Vol. 9; No. 4; 1157-1164; 10.4171/JST/293
• Martínez–Finkelshtein, Andrei; Simanek, Brian; et el. (2019) Poncelet’s theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators; Advances in Mathematics; Vol. 349; 992-1035; 10.1016/j.aim.2019.04.027
• Simon, Barry (2019) Tosio Kato’s Work on Non-Relativistic Quantum Mechanics: An Outline; 10.48550/arXiv.1710.06999
• Simon, Barry (2019) Tosio Kato’s Work on Non-relativistic Quantum Mechanics: A Brief Report; ISBN 9783030126605; Analysis and Operator Theory: Dedicated in Memory of Tosio Kato’s 100th Birthday; Springer International Publishing: Cham, Switzerland; 353-378; 10.1007/978-3-030-12661-2_16
• Simon, Barry (2019) Tosio Kato’s work on non-relativistic quantum mechanics: part 2; Bulletin of Mathematical Sciences; Vol. 9; No. 1; Art. No. 1950005; 10.1007/s13373-018-0121-5
• Christiansen, Jacob S.; Simon, Barry; et el. (2019) Asymptotics of Chebyshev Polynomials, II. DCT Subsets of ℝ; Duke Mathematical Journal; Vol. 168; No. 2; 325-349; 10.1215/00127094-2018-0045
• Breuer, Jonathan; Simon, Barry; et el. (2018) Large Deviations and Sum Rules for Spectral Theory - A Pedagogical Approach; Journal of Spectral Theory; Vol. 8; No. 4; 1551-1581; 10.4171/JST/235
• Breuer, Jonathan; Simon, Barry; et el. (2018) Large Deviations and the Lukic Conjecture; Duke Mathematical Journal; Vol. 167; No. 15; 2857-2902; 10.1215/00127094-2018-0027
• Simon, Barry (2018) The Christoffel-Darboux Kernel; 10.48550/arXiv.0806.1528
• Puhalskii, A. and Simon, Barry (2018) A large-population limit for a Markovian model of group-structured populations; 10.48550/arXiv.1712.09119
• Simon, Barry (2018) Tosio Kato’s work on non-relativistic quantum mechanics: part 1; Bulletin of Mathematical Sciences; Vol. 8; No. 1; 121-232; 10.1007/s13373-018-0118-0
• Simon, Barry (2018) Tosio Kato’s Work on Non-Relativistic Quantum Mechanics: A Brief Report; IAMP News Bulletin; 6-25
• Böttcher, Albrecht; Simon, Barry; et el. (2017) Similarity Between Two Projections; Integral Equations and Operator Theory; Vol. 89; No. 4; 507-518; 10.1007/s00020-017-2414-6
• Frank, Rupert L. and Simon, Barry (2017) Eigenvalue bounds for Schrödinger operators with complex potentials. II; Journal of Spectral Theory; Vol. 7; No. 3; 633-658; 10.4171/JST/173
• Simon, Barry (2017) Unitaries permuting two orthogonal projections; Linear Algebra and its Applications; Vol. 528; 436-441; 10.1016/j.laa.2017.03.026
• Simon, Barry (2017) Equilibrium measures and capacities in spectral theory; 10.48550/arXiv.0711.2700
• Simon, Barry (2017) Ratio asymptotics and weak asymptotic measures for orthogonal polynomials on the real line; Journal of Approximation Theory; Vol. 126; No. 2; 198-217; 10.1016/j.jat.2003.12.002
• Simon, Barry (2017) A Cayley-Hamiltonian Theorem for Periodic Finite Band Matrices; ISBN 978-3-03719-175-0; Functional analysis and operator theory for quantum physics : Pavel Exner anniversary volume; EMS Publishing House: Zurich, Switzerland; 525-529; 10.4171/175-1/25
• Christiansen, Jacob S.; Simon, Barry; et el. (2017) Asymptotics of Chebyshev polynomials, I: subsets of ℝ; Inventiones Mathematicae; Vol. 208; No. 1; 217-245; 10.1007/s00222-016-0689-x
• Frank, Rupert L.; Lemm, Marius; et el. (2017) Condensation of fermion pairs in a domain; Calculus of Variations and Partial Differential Equations; Vol. 56; Art. No. 54; 10.1007/s00526-017-1140-x
• Krüger, Helge and Simon, Barry (2015) Cantor polynomials and some related classes of OPRL; Journal of Approximation Theory; Vol. 191; 71-93; 10.1016/j.jat.2014.04.003
• Simon, Barry (2014) Ed Nelson’s Work in Quantum Theory; ISBN 978-1-4008-6525-3; Diffusion, Quantum Theory, and Radically Elementary Mathematics; Princeton University Press: Princeton, NJ; 75-94; 10.1515/9781400865253.75
• Breuer, Jonathan; Last, Yoram; et el. (2014) Stability of Asymptotics of Christoffel–Darboux Kernels; Communications in Mathematical Physics; Vol. 330; No. 3; 1155-1178; 10.1007/s00220-014-1913-4
• Simon, B. (2013) Spectral Theory of Orthogonal Polynomials; ISBN 9789814449243; XVIIth International Congress on Mathematical Physics; World Scientific Publishing: Hackensack, NJ; 217-228; 10.1142/9789814449243_0012
• Christiansen, Jacob S.; Simon, Barry; et el. (2013) Finite gap Jacobi matrices: A review; ISBN 978-0821875742; Spectral Analysis, Differential Equations and Mathematical Physics; American Mathematical Society: Providence, Rhode Island; 87-103; 10.48550/arXiv.1301.5073
• Holden, Helge; Gesztesy, Fritz; et el. (2013) Spectral analysis, differential equations, and mathematical physics : a festschrift in honor of Fritz Gesztesy’s 60th birthday; ISBN 978-0-8218-7574-2; 10.1090/pspum/087
• Christiansen, Jacob S.; Simon, Barry; et el. (2012) Finite Gap Jacobi Matrices, III. Beyond the Szegő Class; Constructive Approximation; Vol. 35; No. 2; 259-272; 10.1007/s00365-012-9152-4
• Martínez-Finkelshtein, Andrei and Simon, Barry (2011) Asymptotics of the L^2 norm of derivatives of OPUC; Journal of Approximation Theory; Vol. 163; No. 6; 747-778; 10.1016/j.jat.2010.09.002
• Christiansen, Jacob S.; Simon, Barry; et el. (2011) Finite Gap Jacobi Matrices, II. The Szegő Class; Constructive Approximation; Vol. 33; No. 3; 365-403; 10.1007/s00365-010-9094-7
• Frank, Rupert L. and Simon, Barry (2011) Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices; Duke Mathematical Journal; Vol. 157; No. 3; 461-493; 10.1215/00127094-1272912
• Breuer, Jonathan and Simon, Barry (2011) Natural boundaries and spectral theory; Advances in Mathematics; Vol. 226; No. 6; 4902-4920; 10.1016/j.aim.2010.12.019
• Simon, Barry (2011) Convexity: An Analytic Viewpoint; ISBN 9781107007314; 10.1017/CBO9780511910135
• Simon, Barry (2011) On the Removal of Finite Discrete Spectrum by Coefficient Stripping; Journal of Spectral Theory; Vol. 1; No. 1; 81-85; 10.4171/JST/3
• Breuer, Jonathan; Last, Yoram; et el. (2010) The Nevai Condition; Constructive Approximation; Vol. 32; No. 2; 221-254; 10.1007/s00365-009-9055-1
• Christiansen, Jacob S.; Simon, Barry; et el. (2010) Finite Gap Jacobi Matrices, I. The Isospectral Torus; Constructive Approximation; Vol. 32; No. 1; 1-65; 10.1007/s00365-009-9057-z
• Damanik, David; Killip, Rowan; et el. (2010) Perturbations of orthogonal polynomials with periodic recursion coefficients; Annals of Mathematics; Vol. 171; No. 3; 1931-2010; 10.4007/annals.2010.171.1931
• Poltoratski, Alexei; Simon, Barry; et el. (2010) The Hilbert transform of a measure; Journal d’Analyse Mathématique; Vol. 111; No. 1; 247-265; 10.1007/s11854-010-0017-0
• Breuer, Jonathan; Ryckman, Eric; et el. (2010) Equality of the Spectral and Dynamical Definitions of Reflection; Communications in Mathematical Physics; Vol. 295; No. 2; 531-550; 10.1007/s00220-009-0945-7
• Avila, Artur; Last, Yoram; et el. (2010) Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum; Analysis & PDE; Vol. 3; No. 1; 81-108; 10.2140/apde.2010.3.81
• Simon, Barry (2010) Fine Structure of the Zeros of Orthogonal Polynomials: A Progress Report; ISBN 978-0-8218-4803-6; Recent Trends in Orthogonal Polynomials and Approximation Theory; American Mathematical Society: Providence, RI; 241-254
• Simon, Barry (2010) Szegő’s Theorem and Its Descendants: Spectral Theory for L^2 Perturbations of Orthogonal Polynomials; ISBN 9780691147048
• Christiansen, Jacob S.; Simon, Barry; et el. (2009) Finite gap Jacobi matrices: An announcement; Journal of Computational and Applied Mathematics; Vol. 233; No. 3; 652-662; 10.1016/j.cam.2009.02.081
• Cantero, María José and Simon, Barry (2009) Poisson brackets of orthogonal polynomials; Journal of Approximation Theory; Vol. 158; No. 1; 3-48; 10.1016/j.jat.2007.07.001
• Kreimer, Yury; Last, Yoram; et el. (2009) Monotone Jacobi parameters and non-Szegő weights; Journal of Approximation Theory; Vol. 157; No. 2; 144-171; 10.1016/j.jat.2008.04.020
• Simon, Barry (2009) A Celebration of Jürg and Tom; Journal of Statistical Physics; Vol. 134; No. 5-6; 809-812; 10.1007/s10955-008-9627-7
• Simon, Barry (2009) Weak convergence of CD kernels and applications; Duke Mathematical Journal; Vol. 146; No. 2; 305-330; 10.1215/00127094-2008-067
• Simon, Barry (2009) Regularity and the Cesàro–Nevai class; Journal of Approximation Theory; Vol. 156; No. 2; 142-153; 10.1016/j.jat.2008.04.016
• Simon, Barry (2009) Weak convergence of CD kernels and applications; Duke Mathematical Journal; Vol. 146; No. 2; 305-330; 10.1215/00127094-2008-067
• Simon, Barry (2009) Schrödinger operators with purely discrete spectrum; Methods of Functional Analysis and Topology; Vol. 15; No. 1; 61-66
• Killip, Rowan and Simon, Barry (2009) Sum rules and spectral measures of Schrödinger operators with L^2 potentials; Annals of Mathematics; Vol. 170; No. 2; 739-782; 10.48550/arXiv.0608767
• Simon, Barry (2008) Two extensions of Lubinsky’s universality theorem; Journal d’Analyse Mathématique; Vol. 105; No. 1; 345-362; 10.1007/s11854-008-0039-z
• Frank, Rupert L.; Simon, Barry; et el. (2008) Eigenvalue Bounds for Perturbations of Schrödinger Operators and Jacobi Matrices With Regular Ground States; Communications in Mathematical Physics; Vol. 282; No. 1; 199-208; 10.1007/s00220-008-0453-1
• Hundertmark, Dirk and Simon, Barry (2008) Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices; Journal of Mathematical Analysis and Applictions; Vol. 340; No. 2; 892-900; 10.1016/j.jmaa.2007.08.059
• Last, Yoram and Simon, Barry (2008) Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior; Communications on Pure and Applied Mathematics; Vol. 61; No. 4; 486-538; 10.1002/cpa.20185
• Damanik, David; Pushnitski, Alexander; et el. (2008) The Analytic Theory of Matrix Orthogonal Polynomials; Surveys in Approximation Theory; Vol. 4; 1-85; 10.48550/arXiv.0711.2703
• Geszetsy, Fritz; Pushnitski, Alexander; et el. (2008) On the Koplienko Spectral Shift Function. I. Basics; Journal of Mathematical Physics, Analysis and Geometry; Vol. 4; No. 1; 63-107; 10.48550/arXiv.0705.3629
• Simon, Barry (2007) CMV matrices: Five years after; Journal of Computational and Applied Mathematics; Vol. 208; No. 1; 120-154; 10.1016/j.cam.2006.10.033
• Simon, B. (2007) Meromorphic Jost functions and asymptotic expansions for Jacobi parameters; Functional Analysis and its Applications; Vol. 41; No. 2; 143-153; 10.1007/s10688-007-0013-z
• Simon, Barry (2007) Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle; Journal of Mathematical Analysis and Applictions; Vol. 329; No. 1; 376-382; 10.1016/j.jmaa.2006.06.076
• Simon, Barry (2007) Zeros of OPUC and long time asymptotics of Schur and related flows; Inverse Problems and Imaging; Vol. 1; No. 1; 189-215; 10.3934/ipi.2007.1.189
• Simon, Barry (2007) Fine Structure of the Zeros of Orthogonal Polynomials: A Review; ISBN 9789812706430; Proceedings of the international conference, difference equations, special functions and orthogonal polynomials : Munich, Germany, 25-30 July 2005; World Scientific Publishing Co.: Singapore; 636-653; 10.1142/9789812770752_0055
• Simon, Barry (2007) Orthogonal polynomials with exponentially decaying recursion coefficients; ISBN 9780821840894; Probability and mathematical physics : a volume in honor of Stanislav Molchanov; American Mathematical Society: Providence, RI; 453-463; 10.48550/arXiv.0603099
• Last, Yoram and Simon, Barry (2006) The Essential Spectrum of Schrödinger, Jacobi, and CMV Operators; Journal d’Analyse Mathématique; Vol. 98; No. 1; 183-220; 10.1007/BF02790275
• Davies, E. B. and Simon, B. (2006) Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle; Journal of Approximation Theory; Vol. 141; No. 2; 189-213; 10.1016/j.jat.2006.03.006
• Simon, Barry (2006) Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficients; Communications on Pure and Applied Mathematics; Vol. 59; No. 7; 1042-1062; 10.1002/cpa.20106
• Damanik, David and Simon, Barry (2006) Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegő asymptotics; Inventiones Mathematicae; Vol. 165; No. 1; 1-50; 10.1007/s00222-005-0485-5
• Lieb, Elliott H.; Sigal, Israel M.; et el. (2006) Approximate Neutrality of Large-Z Ions; ISBN 354022212X; The Stability of Matter: From Atoms to Stars: Selecta of Elliott H. Lieb; Springer-Verlag: Berlin/Heidelberg; 103-112; 10.1007/3-540-27056-6_9
• Damanik, D. and Simon, B. (2006) Jost functions and Jost solutions for Jacobi matrices, II. Decay and analyticity; International Mathematics Research Notices; Vol. 2006; Art. No. 19396; 10.1155/IMRN/2006/19396
• Simon, Barry (2006) Aizenman’s Theorem for Orthogonal Polynomials on the Unit Circle; Constructive Approximation; Vol. 23; No. 2; 229-240; 10.1007/s00365-005-0599-4
• Simon, Barry (2006) Fine structure of the zeros of orthogonal polynomials, I. A tale of two pictures; Electronic Transactions on Numerical Analysis; Vol. 25; 328-368
• Simon, Barry and Totik, Vilmos (2005) Limits of zeros of orthogonal polynomials on the circle; Mathematische Nachrichten; Vol. 278; No. 12-13; 1615-1620; 10.1002/mana.200410326
• Simon, Barry (2005) Meromorphic Szegő functions and asymptotic series for Verblunsky coefficients; Acta Mathematica; Vol. 195; No. 2; 267-285; 10.1007/BF02588083
• Damanik, David; Killip, Rowan; et el. (2005) Schrödinger Operators with Few Bound States; Communications in Mathematical Physics; Vol. 258; No. 3; 741-750; 10.1007/s00220-005-1366-x
• Simon, Barry (2005) Sturm Oscillation and Comparison Theorems; ISBN 3764370661; Sturm-Liouville Theory; Birkhäuser-Verlag: Basel; 29-43; 10.1007/3-7643-7359-8_2
• Simon, Barry (2005) Fine structure of the zeros of orthogonal polynomials, II. OPUC with competing exponential decay; Journal of Approximation Theory; Vol. 135; No. 1; 125-139; 10.1016/j.jat.2005.04.003
• Simon, Barry (2005) On a theorem of Kac and Gilbert; Journal of Functional Analysis; Vol. 223; No. 1; 109-115; 10.1016/j.jfa.2004.08.015
• Simon, Barry and Zlatoš, Andrej (2005) Higher-order Szegő theorems with two singular points; Journal of Approximation Theory; Vol. 134; No. 1; 114-129; 10.1016/j.jat.2005.02.003
• Simon, Barry (2005) OPUC on one foot; Bulletin of the American Mathematical Society; Vol. 42; No. 4; 431-460; 10.1090/S0273-0979-05-01075-X
• Simon, Barry (2004) A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices; Journal of Functional Analysis; Vol. 214; No. 2; 396-409; 10.1016/j.jfa.2003.11.006
• Gesztesy, Fritz and Simon, Barry (2004) Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schrödinger Operators; Journal of Statistical Physics; Vol. 116; No. 1-4; 361-365; 10.1023/B:JOSS.0000037217.89500.b3
• Hundertmark, Dirk and Simon, Barry (2004) A diamagnetic inequality for semigroup differences; Journal für die reine und angewandte Mathematik (Crelles Journal); Vol. 2004; No. 571; 107-130; 10.1515/crll.2004.036
• Simon, Barry (2004) Orthogonal polynomials on the unit circle: New results; International Mathematics Research Notices; Vol. 2004; No. 53; 2837-2880; 10.1155/S1073792804141664
• Damanik, David; Killip, Rowan; et el. (2004) Necessary and Sufficient Conditions in the Spectral Theory of Jacobi Matrices and Schrödinger Operators; International Mathematics Research Notices; Vol. 2004; No. 22; 1087-1097; 10.1155/S1073792804132790
• Damanik, David; Hundertmark, Dirk; et el. (2003) Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators; Journal of Functional Analysis; Vol. 205; No. 2; 357-379; 10.1016/S0022-1236(03)00070-3
• Simon, Barry and Zlatoš, Andrej (2003) Sum Rules and the Szegő Condition for Orthogonal Polynomials on the Real Line; Communications in Mathematical Physics; Vol. 242; No. 3; 393-423; 10.1007/s00220-003-0906-5
• Killip, Rowan and Simon, Barry (2003) Sum rules for Jacobi matrices and their applications to spectral theory; Annals of Mathematics; Vol. 158; No. 1; 253-321
• Damanik, D.; Hundertmark, D.; et el. (2003) Variational Estimates for Discrete Schrödinger Operators with Potentials of Indefinite Sign; Communications in Mathematical Physics; Vol. 238; No. 3; 545-562; 10.1007/s00220-003-0868-7
• Kiselev, Alexander; Last, Yoram; et el. (2003) Stability of singular spectral types under decaying perturbations; Journal of Functional Analysis; Vol. 198; No. 1; 1-27; 10.1016/S0022-1236(02)00053-8
• Simon, Barry (2003) The Golinskii-Ibragimov Method and a Theorem of Damanik and Killip; International Mathematics Research Notices; Vol. 2003; No. 36; 1973-1986; 10.1155/S107379280313084X
• Hundertmark, Dirk and Simon, Barry (2002) An optimal Lᵖ-bound on the Krein spectral shift function; Journal d’Analyse Mathématique; Vol. 87; No. 1; 199-208; 10.1007/BF02868474
• Hundertmark, Dirk and Simon, Barry (2002) Lieb–Thirring Inequalities for Jacobi Matrices; Journal of Approximation Theory; Vol. 118; No. 1; 106-130; 10.1006/jath.2002.3704
• Kirsch, Werner and Simon, Barry (2001) Approach to equilibrium for a forced Burgers equation; Journal of Evolution Equations; Vol. 1; No. 4; 411-419; 10.1007/PL00001380
• Simon, Barry (2000) Resonances in One Dimension and Fredholm Determinants; Journal of Functional Analysis; Vol. 178; No. 2; 396-420; 10.1006/jfan.2000.3669
• Ramm, Alexander and Simon, Barry (2000) A new approach to inverse spectral theory, III. Short-range potentials; Journal d’Analyse Mathématique; Vol. 80; No. 1; 319-334; 10.1007/BF02791540
• Geszetsy, Fritz and Simon, Barry (2000) A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure; Annals of Mathematics; Vol. 152; No. 2; 593-643; 10.2307/2661393
• Gesztesy, Fritz and Simon, Barry (2000) Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum; Transactions of the American Mathematical Society; Vol. 352; No. 6; 2765-2787; 10.1090/S0002-9947-99-02544-1
• Simon, Barry (2000) Schrödinger operators in the twentieth century; Journal of Mathematical Physics; Vol. 41; No. 6; 3523-3555; 10.1063/1.533321
• Cordes, Heinz; Jensen, Arne; et el. (2000) Tosio Kato (1917–1999); Notices of the American Mathematical Society; Vol. 47; No. 6; 650-657
• Gesztesy, Fritz and Simon, Barry (2000) On Local Borg–Marchenko Uniqueness Results; Communications in Mathematical Physics; Vol. 211; No. 2; 273-287; 10.1007/s002200050812
• Simon, Barry (1999) A new approach to inverse spectral theory, I. Fundamental formalism; Annals of Mathematics; Vol. 150; No. 3; 1029-1057; 10.2307/121061
• Kiselev, Alexander; Remling, Christian; et el. (1999) Effective Perturbation Methods for One-Dimensional Schrödinger Operators; Journal of Differential Equations; Vol. 151; No. 2; 290-312; 10.1006/jdeq.1998.3514
• Last, Yoram and Simon, Barry (1999) Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators; Inventiones Mathematicae; Vol. 135; No. 2; 329-367; 10.1007/s002220050288
• Gesztesy, Fritz and Simon, Barry (1999) On the determination of a potential from three spectra; ISBN 978-0-8218-1387-4; Differential Operators and Spectral Theory; American Mathematical Society: Province; 85-92; 10.1090/trans2/189
• Simon, Barry (1998) The Classical Moment Problem as a Self-Adjoint Finite Difference Operator; Advances in Mathematics; Vol. 137; No. 1; 82-203; 10.1006/aima.1998.1728
• Kiselev, Alexander; Last, Yoram; et el. (1998) Modified Prüfer and EFGP Transforms and the Spectral Analysis of One-Dimensional Schrödinger Operators; Communications in Mathematical Physics; Vol. 194; No. 1; 1-45; 10.1007/s002200050346
• Simon, Barry (1998) Spectral averaging and the Krein spectral shift; Proceedings of the American Mathematical Society; Vol. 126; No. 5; 1409-1413; 10.1090/S0002-9939-98-04261-0
• Last, Yoram and Simon, Barry (1998) Modified Prüfer and EFGP Transforms and Deterministic Models with Dense Point Spectrum; Journal of Functional Analysis; Vol. 154; No. 2; 513-530; 10.1006/jfan.1997.3192
• del Rio, Rafael and Simon, Barry (1997) Point spectrum and mixed spectral types for rank one perturbations; Proceedings of the American Mathematical Society; Vol. 125; No. 12; 3593-3599; 10.1090/S0002-9939-97-03997-X
• Gesztesy, Fritz and Simon, Barry (1997) m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices; Journal d’Analyse Mathématique; Vol. 73; No. 1; 267-297; 10.1007/BF02788147
• del Rio, Rafael; Gesztesy, Fritz; et el. (1997) Inverse spectral analysis with partial information on the potential. III. Updating boundary conditions; International Mathematics Research Notices; Vol. 1997; No. 15; 751-758; 10.1155/S1073792897000494
• Truhlar, Donald G. and Simon, Barry (1997) Multiparticle Quantum Scattering With Applications to Nuclear, Atomic and Molecular Physics; ISBN 978-1-4612-7318-9; Multiparticle Quantum Scattering With Applications to Nuclear, Atomic and Molecular Physics; Springer: New York, NY; 10.1007/978-1-4612-1870-8
• Del Rio, R.; Jitomirskaya, S.; et el. (1996) Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization; Journal d’Analyse Mathématique; Vol. 69; No. 1; 153-200; 10.1007/BF02787106
• Gesztesy, F.; Simon, B.; et el. (1996) Spectral deformations of one-dimensional Schrödinger operators; Journal d’Analyse Mathématique; Vol. 70; No. 1; 267-324; 10.1007/BF02820446
• Gesztesy, F.; Holden, H.; et el. (1996) A Trace Formula for Multidimensional Schrödinger Operators; Journal of Functional Analysis; Vol. 141; No. 2; 449-465; 10.1006/jfan.1996.0137
• Simon, Barry (1996) Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators; Proceedings of the American Mathematical Society; Vol. 124; No. 11; 3361-3369; 10.1090/S0002-9939-96-03599-X
• Simon, Barry and Zhu, Yunfeng (1996) The Lyapunov Exponents for Schrödinger Operators with Slowly Oscillating Potentials; Journal of Functional Analysis; Vol. 140; No. 2; 541-556; 10.1006/jfan.1996.0117
• Simon, B. and Stolz, G. (1996) Operators with singular continuous spectrum, V. Sparse potentials; Proceedings of the American Mathematical Society; Vol. 124; No. 7; 2073-2080; 10.1090/S0002-9939-96-03465-X
• Gesztesy, F.; Simon, B.; et el. (1996) Zeros of the Wronskian and Renormalized Oscillation Theory; American Journal of Mathematics; Vol. 118; No. 3; 571-594; 10.1353/ajm.1996.0024
• Simon, Barry (1996) [Operators with singular continuous spectrum,

6. Graph Laplacians and Laplace-Beltrami operators](https://resolver.caltech.edu/CaltechAUTHORS:20180320-112111420); Proceedings of the American Mathematical Society; Vol. 124; No. 4; 1177-1183; 10.1090/S0002-9939-96-03245-5

• Simon, Barry (1996) [Operators with Singular Continuous Spectrum,

7. Examples with Borderline Time Decay](https://resolver.caltech.edu/CaltechAUTHORS:20180315-112637401); Communications in Mathematical Physics; Vol. 176; No. 3; 713-722; 10.1007/BF02099257

• Gesztesy, F. and Simon, B. (1996) Uniqueness theorems in inverse spectral theory for one-dimensional Schrödinger operators; Transactions of the American Mathematical Society; Vol. 348; No. 1; 349-373; 10.1090/S0002-9947-96-01525-5
• Simon, B. (1995) L^p Norms of the Borel Transform and the Decomposition of Measures; Proceedings of the American Mathematical Society; Vol. 123; No. 12; 3749-3755; 10.2307/2161903
• Hof, A.; Knill, O.; et el. (1995) Singular Continuous Spectrum for Palindromic Schrödinger Operators; Communications in Mathematical Physics; Vol. 174; No. 1; 149-159; 10.1007/BF02099468
• Del Rio, R.; Jitomirskaya, S.; et el. (1995) What is Localization?; Physical Review Letters; Vol. 75; No. 1; 117-119; 10.1103/PhysRevLett.75.117
• Kiselev, A. and Simon, B. (1995) Rank One Perturbations with Infinitesimal Coupling; Journal of Functional Analysis; Vol. 130; No. 2; 345-356; 10.1006/jfan.1995.1074
• Gesztesy, F.; Holden, H.; et el. (1995) Absolute Summability of the Trace Relation for Certain Schrödinger Operators; Communications in Mathematical Physics; Vol. 168; No. 1; 137-161; 10.1007/BF02099586
• Gesztesy, F. and Simon, B. (1995) Rank One Perturbations at Infinite Coupling; Journal of Functional Analysis; Vol. 128; No. 1; 245-252; 10.1006/jfan.1995.1030
• Simon, Barry (1995) Operators with Singular Continuous Spectrum: I. General Operators; Annals of Mathematics; Vol. 141; No. 1; 131-145
• Gesztesy, F.; Holden, H.; et el. (1995) Higher order trace relations for Schrödinger operators; Reviews in Mathematical Physics; Vol. 7; No. 6; 893-922; 10.1142/S0129055X95000347
• Del Rio, R.; Makarov, N.; et el. (1994) Operators with singular continuous spectrum: II. Rank one operators; Communications in Mathematical Physics; Vol. 165; No. 1; 59-67; 10.1007/BF02099737
• Jitomirskaya, S. and Simon, B. (1994) Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators; Communications in Mathematical Physics; Vol. 165; No. 1; 201-205; 10.1007/BF02099743
• Del Rio, R.; Jitomirskaya, S.; et el. (1994) Singular continuous spectrum is generic; Bulletin of the American Mathematical Society; Vol. 31; No. 2; 208-212; 10.1090/S0273-0979-1994-00518-X
• Avron, J.; Seiler, R.; et el. (1994) The Index of a Pair of Projections; Journal of Functional Analysis; Vol. 120; No. 1; 220-237; 10.1006/jfan.1994.1031
• Avron, Joseph E.; Seiler, Ruedi; et el. (1994) Charge deficiency, charge transport and comparison of dimensions; Communications in Mathematical Physics; Vol. 159; No. 2; 399-422; 10.1007/BF02102644
• Simon, Barry (1994) Cyclic vectors in the Anderson model; Reviews in Mathematical Physics; Vol. 6; No. 5a; 1183-1185; 10.1142/S0129055X94000420
• del Rio, R.; Simon, B.; et el. (1994) Stability of Spectral Types for Sturm-Liouville Operators; Mathematical Research Letters; Vol. 1; No. 4; 437-450; 10.4310/MRL.1994.v1.n4.a4
• Gesztesy, F.; Holden, H.; et el. (1993) On the Toda and Kac-van Moerbeke systems; Transactions of the American Mathematical Society; Vol. 339; No. 2; 849-868; 10.1090/S0002-9947-1993-1153014-1
• Gordon, Y. A.; Jakšić, V.; et el. (1993) Spectral Properties of Random Schrödinger Operators with Unbounded Potentials; Communications in Mathematical Physics; Vol. 157; No. 1; 23-50; 10.1007/BF02098017
• Gesztesy, F.; Holden, H.; et el. (1993) Trace formulae and inverse spectral theory for Schrödinger operators; Bulletin of the American Mathematical Society; Vol. 29; No. 2; 250-256; 10.1090/S0273-0979-1993-00431-2
• Simon, Barry (1993) Large time behavior of the heat kernel: on a theorem of Chavel and Karp; Proceedings of the American Mathematical Society; Vol. 118; No. 2; 513-514; 10.1090/S0002-9939-1993-1139473-4
• Graf, Gian Michele and Simon, B. (1993) Asymptotic Series for the Ground State Energy of Schrödinger Operators; Journal of Functional Analysis; Vol. 112; No. 2; 442-446; 10.1006/jfan.1993.1039
• Gesztesy, F. and Simon, B. (1993) A Short Proof of Zheludev’s Theorem; Transactions of the American Mathematical Society; Vol. 335; No. 1; 329-340
• Simon, Barry (1992) The Weyl Transform and L^p Functions on Phase Space; Proceedings of the American Mathematical Society; Vol. 116; No. 4; 1045-1047
• Simon, Barry (1992) Best constants in some operator smoothness estimates; Journal of Functional Analysis; Vol. 107; No. 1; 66-71; 10.1016/0022-1236(92)90100-W
• Jakšić, V.; Molčanov, S.; et el. (1992) Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps; Journal of Functional Analysis; Vol. 106; No. 1; 59-79; 10.1016/0022-1236(92)90063-O
• Davies, E. B. and Simon, B. (1992) Spectral properties of Neumann Laplacian of horns; Geometric and Functional Analysis; Vol. 2; No. 1; 105-117; 10.1007/BF01895707
• Simon, Barry (1992) The Neumann Laplacian of a jelly roll; Proceedings of the American Mathematical Society; Vol. 114; No. 3; 783-785; 10.1090/S0002-9939-1992-1076578-X
• Gesztesy, F.; Graf, G. M.; et el. (1992) The ground state energy of Schrödinger operators; Communications in Mathematical Physics; Vol. 150; No. 2; 375-384
• Hempel, Rainer; Seco, Luis A.; et el. (1991) The essential spectrum of Neumann Laplacians on some bounded singular domains; Journal of Functional Analysis; Vol. 102; No. 2; 448-483; 10.1016/0022-1236(91)90130-W
• Davies, E. B. and Simon, B. (1991) L^p norms of non-critical Schrödinger semigroups; Journal of Functional Analysis; Vol. 102; No. 1; 95-115; 10.1016/0022-1236(91)90137-T
• Gesztesy, F.; Holden, H.; et el. (1991) Explicit construction of solutions of the modified Kadomtsev-Petviashvili equation; Journal of Functional Analysis; Vol. 98; No. 1; 211-228; 10.1016/0022-1236(91)90096-N
• Gesztesy, F.; Schweiger, W.; et el. (1991) Commutation methods applied to the mKdV-equation; Transactions of the American Mathematical Society; Vol. 324; No. 2; 465-525; 10.1090/S0002-9947-1991-1029000-7
• Simon, Barry (1990) Absence of Ballistic Motion; Communications in Mathematical Physics; Vol. 134; No. 1; 209-212; 10.1007/BF02102095
• Avron, Joseph E.; Seiler, Ruedi; et el. (1990) Quantum Hall effect and the relative index for projections; Physical Review Letters; Vol. 65; No. 17; 2185-2188; 10.1103/PhysRevLett.65.2185
• Avron, J.; v. Mouche, P. H. M.; et el. (1990) On the measure of the spectrum for the almost Mathieu operator; Communications in Mathematical Physics; Vol. 132; No. 1; 103-118; 10.1007/BF02278001
• Carmona, René; Masters, Wen Chen; et el. (1990) Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions; Journal of Functional Analysis; Vol. 91; No. 1; 117-142; 10.1016/0022-1236(90)90049-Q
• Gesztesy, F. and Simon, Barry (1990) Constructing solutions of the mKdV-equation; Journal of Functional Analysis; Vol. 89; No. 1; 53-60; 10.1016/0022-1236(90)90003-4
• Lieb, Elliott H.; Sigal, Israel M.; et el. (1988) Approximate neutrality of large-Z ions; Communications in Mathematical Physics; Vol. 116; No. 4; 635-644; 10.1007/bf01224904
• Avron, J. E.; Sadun, L.; et el. (1988) Topological Invariants in Fermi Systems with Time-Reversal Invariance; Physical Review Letters; Vol. 61; No. 12; 1329-1332; 10.1103/PhysRevLett.61.1329
• Englisch, H.; Kirsch, W.; et el. (1988) Density of Surface States in Discrete Models; Physical Review Letters; Vol. 61; No. 11; 1261-1262; 10.1103/PhysRevLett.61.1261
• Bollé, D.; Gesztesy, F.; et el. (1987) Witten index, axial anomaly, and Krein’s spectral shift function in supersymmetric quantum mechanics; Journal of Mathematical Physics; Vol. 28; No. 7; 1512-1525; 10.1063/1.527508
• Simon, Barry (1986) Schrödinger semigroups on the scale of Sobolev spaces; Pacific Journal of Mathematics; Vol. 122; No. 2; 475-480
• Simon, Barry; Taylor, Michael; et el. (1985) Some Rigorous Results for the Anderson Model; Physical Review Letters; Vol. 54; No. 14; 1589-1592; 10.1103/PhysRevLett.54.1589
• Simon, Barry (1985) Almost periodic Schrödinger operators IV. The Maryland model; Annals of Physics; Vol. 159; No. 1; 157-183; 10.1016/0003-4916(85)90196-4
• Simon, Barry (1985) Some aspects of the theory of Schrödinger operators; ISBN 9783540160359; Schrödinger Operators; Springer: Berlin, Heidelberg; 177-203; 10.1007/bfb0080333
• Simon, Barry (1984) Semiclassical analysis of low lying elgenvalues. III. Width of the ground state band in strongly coupled solids; Annals of Physics; Vol. 158; No. 2; 415-420; 10.1016/0003-4916(84)90125-8
• Delyon, Francois; Simon, Barry; et el. (1984) From Power-Localized to Extended States in a Class of One-Dimensional Disordered Systems; Physical Review Letters; Vol. 52; No. 24; 2187-2189; 10.1103/PhysRevLett.52.2187
• Harrell, Evans M.; Corngold, Noel; et el. (1984) The mathematical theory of resonances whose widths are exponentially small, II; Journal of Mathematical Analysis and Applictions; Vol. 99; No. 2; 447-457; 10.1016/0022-247X(84)90225-7
• Lieb, Elliott H.; Sigal, Israel M.; et el. (1984) Asymptotic Neutrality of Large-Z Ions; Physical Review Letters; Vol. 52; No. 12; 994-996; 10.1103/PhysRevLett.52.994
• Simon, Barry (1983) Holonomy, the Quantum Adiabatic Theorem, and Berry’s Phase; Physical Review Letters; Vol. 51; No. 24; 2167-2170; 10.1103/PhysRevLett.51.2167
• Avron, J. E.; Seiler, R.; et el. (1983) Homotopy and Quantization in Condensed Matter Physics; Physical Review Letters; Vol. 51; No. 1; 51-53; 10.1103/PhysRevLett.51.51
• Avron, J.; Craig, W.; et el. (1983) Large coupling behaviour of the Lyapunov exponent for tight binding one-dimensional random systems; Journal of Physics A: Mathematical and General; Vol. 16; No. 7; L209-L211; 10.1088/0305-4470/16/7/002
• Simon, Barry (1983) Equality of the density of states in a wide class of tight-binding Lorentzian random models; Physical Review B; Vol. 27; No. 6; 3859-3860; 10.1103/PhysRevB.27.3859
• Simon, Barry (1983) Some quantum operators with discrete spectrum but classically continuous spectrum; Annals of Physics; Vol. 146; No. 1; 209-220; 10.1016/0003-4916(83)90057-X
• Simon, Barry (1982) Almost periodic Schrödinger operators: A Review; Advances in Applied Mathematics; Vol. 3; No. 4; 463-490; 10.1016/s0196-8858(82)80018-3
• Simon, Barry (1982) Continuity of the density of states in a magnetic field; Journal of Physics A: Mathematical and General; Vol. 15; No. 9; 2981-2983; 10.1088/0305-4470/15/9/043
• Simon, Barry (1982) Almost periodic Schröder operators: A review; ISBN 9783540111924; Mathematical Problems in Theoretical Physics; Springer Berlin Heidelberg: Berlin, Heidelberg; 157; 10.1007/3-540-11192-1_30
• Simon, Barry (1981) Spectrum and continuum eigenfunctions of Schrödinger operators; Journal of Functional Analysis; Vol. 42; No. 3; 347-355; 10.1016/0022-1236(81)90094-X
• Avron, Joseph and Simon, Barry (1981) The Asymptotics of the Gap in the Mathieu Equation; Annals of Physics; Vol. 134; No. 1; 76-84; 10.1016/0003-4916(81)90005-1
• Avron, Joseph E. and Simon, Barry (1981) Almost Periodic Hill’s Equation and the Rings of Saturn; Physical Review Letters; Vol. 46; No. 17; 1166-1168; 10.1103/PhysRevLett.46.1166
• Simon, Barry (1981) Pointwise domination of matrices and comparison of ℐ_p norms; Pacific Journal of Mathematics; Vol. 97; No. 2; 471-475
• Klaus, M. and Simon, Barry (1980) Coupling Constant Thresholds in Nonrelativistic Quantum Mechanics. I. Short-Range Two-Body Case; Annals of Physics; Vol. 130; No. 2; 251-281; 10.1016/0003-4916(80)90338-3
• Schecter, M. and Simon, B. (1980) Unique continuation for Schrodinger operators with unbounded potentials; Journal of Mathematical Analysis and Applictions; Vol. 77; No. 2; 482-492; 10.1016/0022-247X(80)90242-5
• Miller, Keith and Simon, Barry (1980) Quantum Magnetic Hamiltonians with Remarkable Spectral Properties; Physical Review Letters; Vol. 44; No. 25; 1706-1707; 10.1103/PhysRevLett.44.1706
• Simon, Barry (1980) Decay of Correlations in Ferromagnets; Physical Review Letters; Vol. 44; No. 8; 547-549; 10.1103/PhysRevLett.44.547
• Enss, V. and Simon, B. (1980) Bounds on Total Cross Sections in Atom-Atom and Atom-Ion Collisions by Geometric Methods; Physical Review Letters; Vol. 44; No. 5; 319-322; 10.1103/PhysRevLett.44.319
• Avron, J. E.; Herbst, I. W.; et el. (1979) Strongly bound states of hydrogen in intense magnetic field; Physical Review A; Vol. 20; No. 6; 2287-2296; 10.1103/PhysRevA.20.2287
• Benassi, L.; Grecchi, V.; et el. (1979) Bender-Wu Formula and the Stark Effect in Hydrogen; Physical Review Letters; Vol. 42; No. 11; 704-707; 10.1103/PhysRevLett.42.704
• Herbst, I. W. and Simon, B. (1978) Stark Effect Revisited; Physical Review Letters; Vol. 41; No. 2; 67-69; 10.1103/PhysRevLett.41.67
• Avron, J.; Herbst, I.; et el. (1977) Formation of Negative Ions in Magnetic Fields; Physical Review Letters; Vol. 39; No. 17; 1068-1070; 10.1103/PhysRevLett.39.1068
• Dyson, Freeman J.; Lieb, Elliott H.; et el. (1976) Phase Transitions in the Quantum Heisenberg Model; Physical Review Letters; Vol. 37; No. 3; 120-123; 10.1103/PhysRevLett.37.120
• Simon, Barry (1976) Universal Diamagnetism of Spinless Bose Systems; Physical Review Letters; Vol. 36; No. 18; 1083-1084; 10.1103/PhysRevLett.36.1083
• Seiler, E. and Simon, B. (1975) An inequality among determinants; Proceedings of the National Academy of Sciences of the United States of America; Vol. 72; No. 9; 3277-3278; PMCID PMC432972
• Lieb, Elliott H. and Simon, Barry (1973) Thomas-Fermi Theory Revisited; Physical Review Letters; Vol. 31; No. 11; 681-683; 10.1103/PhysRevLett.31.681
• Simon, Barry and Griffiths, Robert

2. 1973. Griffiths-Hurst-Sherman Inequalities and a Lee-Yang Therorem for the(ϕ^4)_2 Field Theory; Physical Review Letters; Vol. 30; No. 19; 931-933; 10.1103/PhysRevLett.30.931

• Simon, Barry (1972) Summability Methods, the Strong Asymptotic Condition, and Unitarity in Quantum Field Theory; Physical Review Letters; Vol. 28; No. 17; 1145-1146; 10.1103/PhysRevLett.28.1145
• Simon, Barry (1970) Borel Summability of the Ground-State Energy in Spatially Cutoff (ϕ^4)_2; Physical Review Letters; Vol. 25; No. 22; 1583-1586; 10.1103/PhysRevLett.25.1583
• Simon, Barry (1970) Some Comments on the Jin-Martin Lower Bound; Physical Review D; Vol. 1; No. 4; 1240-1241; 10.1103/PhysRevD.1.1240
• Loeffel, J. J.; Martin, A.; et el. (1969) Pade approximants and the anharmonic oscillator; Physics Letters B; Vol. 30; No. 9; 656-658; 10.1016/0370-2693(69)90087-2
• Simon, Barry (1969) On the Growth of the Ground‐State Binding Energy with Increase in Potential Strength; Journal of Mathematical Physics; Vol. 10; No. 8; 1415-1421; 10.1063/1.1664983
• Simon, Barry (1969) On the Growth of the Number of Bound States with Increase in Potential Strength; Journal of Mathematical Physics; Vol. 10; No. 7; 1123-1126; 10.1063/1.1664948
• Simon, B. (1969) Convergence of regularized, renormalized perturbation series for super-renormalizable field theories; Il Nuovo Cimento A Series 10; Vol. 59; No. 1; 199-214; 10.1007/bf02756356