- 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,
- 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,
- 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
- 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