# zbMATH — the first resource for mathematics

## Simon, Barry

Compute Distance To:
 Author ID: simon.barry.1 Published as: Simon; Simon, B.; Simon, Barry Homepage: http://math.caltech.edu/simon/simon.html External Links: MGP · Math-Net.Ru · Wikidata · ResearchGate · dblp · GND
 Documents Indexed: 356 Publications since 1968, including 34 Books Biographic References: 7 Publications
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#### Co-Authors

 150 single-authored 32 Gesztesy, Fritz 16 Avron, Joseph E. 12 Last, Yoram 10 Reed, Michael C. 9 Davies, Edward Brian 9 Holden, Helge 9 Zinchenko, Maxim 8 Christiansen, Jacob Stordal 8 Damanik, David 8 Kirsch, Werner 7 Breuer, Jonathan 7 del Río Castillo, Rafael René 6 Hundertmark, Dirk 6 Killip, Rowan 5 Jitomirskaya, Svetlana Ya. 4 Deift, Percy A. 4 Frank, Rupert L. 4 Herbst, Ira W. 4 Kiselev, Alexander A. 4 Teschl, Gerald 4 Zhao, Zhongxin 3 Carmona, René A. 3 Craig, Walter 3 Harrell, Evans M. II 3 Hoffmann-Ostenhof, Maria 3 Hoffmann-Ostenhof, Thomas 3 Klaus, Martin 3 Kotani, Shinichi 3 Kurasov, Pavel B. 3 Laptev, Ari 3 Lieb, Elliott H. 3 Molchanov, Stanislav Alekseevich 3 Naboko, Serguei N. 3 Souillard, Bernard 2 Alonso, Alberto 2 Bollé, D. 2 Delyon, François 2 Enss, Volker 2 Gordon, Alexander Ya. 2 Graf, Gian Michele 2 Grosse, Harald 2 Guerra, Francesco 2 Jakšić, Vojkan 2 Makarov, Nikolai Georgievich 2 Martínez-Finkelshtein, Andrei 2 Perry, Peter A. 2 Pushnitski, Alexander B. 2 Rosen, Jay S. 2 Rosen, Lon M. 2 Sadun, L. 2 Schweiger, Wolfgang 2 Seiler, Ruedi 2 Sigal, Israel Michael 2 Stolz, Gunter 2 Taylor, Michael Eugene 2 Zeitouni, Ofer 2 Zlatoš, Andrej 1 Aizenman, Michael 1 Avila Cordeiro de Melo, Artur 1 Avni, Nir 1 Bellissard, Jean V. 1 Bentosela, François 1 Böttcher, Albrecht 1 Bulla, W. 1 Cantero, María José 1 Cordes, Heinz Otto 1 Corngold, Noel 1 Cycon, Hans L. 1 Davies, Ian M. 1 Denisov, Sergey A. 1 Duclos, Pierre 1 Englisch, Harald 1 Faris, William G. 1 Friedland, Shmuel 1 Froese, Richard 1 Fröhling, Jüerg 1 Graffi, Sandro 1 Grecchi, Vincenzo 1 Gross, Leonard 1 Gurarie, David 1 Hempel, Rainer 1 Hepp, Klaus 1 Høegh-Krohn, Raphael J. 1 Hof, A. L. 1 Howland, James S. 1 Hunziker, Willi 1 Jaffe, Arthur 1 Jensen, Arne 1 Knill, Oliver 1 Kreimer, Yury 1 Krüger, Helge 1 Kuroda, Shige Toshi 1 Lemm, Marius 1 Masters, Wen Chen 1 Miller, Keith D. 1 Nappi, Chiara R. 1 Nelson, Joseph Edward 1 Poltoratski, Alexei G. 1 Ponce, Gustavo 1 Radin, Charles ...and 34 more Co-Authors
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#### Serials

 52 Communications in Mathematical Physics 39 Journal of Functional Analysis 20 Proceedings of the American Mathematical Society 11 Duke Mathematical Journal 11 Journal of Approximation Theory 9 Annals of Mathematics. Second Series 8 Journal d’Analyse Mathématique 8 Advances in Mathematics 8 Transactions of the American Mathematical Society 8 Annals of Physics 8 Bulletin of the American Mathematical Society. New Series 6 Communications on Pure and Applied Mathematics 6 IMRN. International Mathematics Research Notices 5 Journal of Statistical Physics 5 Constructive Approximation 5 Journal of Physics A: Mathematical and General 4 Journal of Mathematical Analysis and Applications 4 Journal of Spectral Theory 4 Princeton Series in Physics 3 American Mathematical Monthly 3 Journal of Mathematical Physics 3 Acta Mathematica 3 Inventiones Mathematicae 3 Journal of Computational and Applied Mathematics 3 Pacific Journal of Mathematics 3 Journal of Operator Theory 3 Notices of the American Mathematical Society 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Physical Review Letters 2 Reviews in Mathematical Physics 2 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 2 Indiana University Mathematics Journal 2 Journal of Differential Equations 2 Mathematische Annalen 2 Mathematische Zeitschrift 2 Advances in Applied Mathematics 2 Linear Algebra and its Applications 2 Bulletin of the American Mathematical Society 2 Colloquium Publications. American Mathematical Society 2 The IMA Volumes in Mathematics and its Applications 2 Inverse Problems and Imaging 1 Archive for Rational Mechanics and Analysis 1 Helvetica Physica Acta 1 Letters in Mathematical Physics 1 American Journal of Mathematics 1 The Annals of Probability 1 Functional Analysis and its Applications 1 Integral Equations and Operator Theory 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Nachrichten 1 Geometric and Functional Analysis. GAFA 1 Pokroky Matematiky, Fyziky & Astronomie 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Calculus of Variations and Partial Differential Equations 1 ETNA. Electronic Transactions on Numerical Analysis 1 Mathematical Research Letters 1 Methods of Functional Analysis and Topology 1 Journal of Evolution Equations 1 Surveys in Approximation Theory (SAT) 1 Journal of Mathematical Physics, Analysis, Geometry 1 Cambridge Tracts in Mathematics 1 Graduate Studies in Mathematics 1 Grundlehren der Mathematischen Wissenschaften 1 London Mathematical Society Lecture Note Series 1 Mathematical Surveys and Monographs 1 Proceedings of Symposia in Pure Mathematics 1 Analysis & PDE 1 Bulletin of Mathematical Sciences 1 Operator Theory: Advances and Applications
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#### Fields

 163 Operator theory (47-XX) 115 Partial differential equations (35-XX) 88 Quantum theory (81-XX) 68 Ordinary differential equations (34-XX) 47 Harmonic analysis on Euclidean spaces (42-XX) 36 Probability theory and stochastic processes (60-XX) 34 Functional analysis (46-XX) 25 Functions of a complex variable (30-XX) 18 Special functions (33-XX) 15 Difference and functional equations (39-XX) 14 Statistical mechanics, structure of matter (82-XX) 13 General and overarching topics; collections (00-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 History and biography (01-XX) 10 Real functions (26-XX) 6 Combinatorics (05-XX) 6 Measure and integration (28-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Potential theory (31-XX) 5 Approximations and expansions (41-XX) 4 General topology (54-XX) 3 Topological groups, Lie groups (22-XX) 3 Numerical analysis (65-XX) 3 Mechanics of particles and systems (70-XX) 3 Optics, electromagnetic theory (78-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Group theory and generalizations (20-XX) 2 Integral transforms, operational calculus (44-XX) 2 Differential geometry (53-XX) 2 Fluid mechanics (76-XX) 1 Field theory and polynomials (12-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Manifolds and cell complexes (57-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH

327 Publications have been cited 19,244 times in 11,901 Documents Cited by Year
Methods of modern mathematical physics. IV: Analysis of operators. Zbl 0401.47001
Reed, Michael; Simon, Barry
1978
Methods of modern mathematical physics. II: Fourier analysis, self- adjointness. Zbl 0308.47002
Reed, Michael; Simon, Barry
1975
Methods of modern mathematical physics. 1: Functional analysis. Zbl 0242.46001
Reed, Michael; Simon, Barry
1972
Methods of modern mathematical physics. I: Functional analysis. Rev. and enl. ed. Zbl 0459.46001
Reed, Michael; Simon, Barry
1980
Methods of modern mathematical physics. III: Scattering theory. Zbl 0405.47007
Reed, Michael; Simon, Barry
1979
Schrödinger operators, with application to quantum mechanics and global geometry. Zbl 0619.47005
Cycon, H. L.; Froese, R. G.; Kirsch, W.; Simon, B.
1987
Schrödinger semigroups. Zbl 0524.35002
Simon, Barry
1982
Trace ideals and their applications. Zbl 0423.47001
Simon, Barry
1979
Functional integration and quantum physics. Zbl 0434.28013
Simon, Barry
1979
Trace ideals and their applications. 2nd ed. Zbl 1074.47001
Simon, Barry
2005
Orthogonal polynomials on the unit circle. Part 1: Classical theory. Zbl 1082.42020
Simon, Barry
2005
The $$P(\phi )_{2}$$ Euclidean (quantum) field theory. Zbl 1175.81146
Simon, Barry
1974
Schrödinger operators with magnetic fields. I: General interactions. Zbl 0399.35029
Avron, J.; Herbst, I.; Simon, B.
1978
Brownian motion and Harnack inequality for Schrödinger operators. Zbl 0459.60069
Aizenman, M.; Simon, B.
1982
Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians. Zbl 0568.47034
Davies, E. B.; Simon, B.
1984
The classical moment problem as a self-adjoint finite difference operator. Zbl 0910.44004
Simon, Barry
1998
The Thomas-Fermi theory of atoms, molecules and solids. Zbl 0938.81568
Lieb, Elliott H.; Simon, Barry
1977
Orthogonal polynomials on the unit circle. Part 2: Spectral theory. Zbl 1082.42021
Simon, Barry
2005
Quantum mechanics for Hamiltonians defined as quadratic forms. Zbl 0232.47053
Simon, Barry
1971
Spectral analysis of N-body Schrödinger operators. Zbl 0477.35069
Perry, P.; Sigal, I. M.; Simon, B.
1981
The bound state of weakly coupled Schrödinger operators in one and two dimensions. Zbl 0325.35029
Simon, Barry
1976
Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Zbl 0609.47001
Simon, Barry; Wolff, Tom
1986
Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory. Zbl 0252.47009
Simon, Barry
1973
Almost periodic Schrödinger operators. II: The integrated density of states. Zbl 0544.35030
Avron, Joseph; Simon, Barry
1983
Sum rules for Jacobi matrices and their applications to spectral theory. Zbl 1050.47025
Killip, Rowan; Simon, Barry
2003
Inverse spectral analysis with partial information on the potential. II: The case of discrete spectrum. Zbl 0948.34060
Gesztesy, Fritz; Simon, Barry
2000
Hypercontra ctive semigroups and two dimensional self-coupled Bose fields. Zbl 0241.47029
Simon, Barry; Høegh-Krohn, Raphael
1972
Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions. Zbl 0716.35006
Carmona, René; Masters, Wen Chen; Simon, Barry
1990
Szegő’s theorem and its descendants. Spectral theory for $$L^2$$ perturbations of orthogonal polynomials. Zbl 1230.33001
Simon, Barry
2011
A canonical decomposition for quadratic forms with applications to monotone convergence theorems. Zbl 0413.47029
Simon, Barry
1978
Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators. Zbl 0931.34066
Last, Yoram; Simon, Barry
1999
The statistical mechanics of lattice gases. Vol. I. Zbl 0804.60093
Simon, Barry
1993
Operators with singular continuous spectrum. IV: Hausdorff dimensions, rank one perturbations, and localization. Zbl 0908.47002
del Rio, Rafael; Jitomirskaya, S.; Last, Y.; Simon, Barry
1996
The index of a pair of projections. Zbl 0822.47033
Avron, Joseph E.; Seiler, Ruedi; Simon, Barry
1994
Notes on infinite determinants of Hilbert space operators. Zbl 0353.47008
Simon, Barry
1977
Semiclassical analysis of low lying eigenvalues. II: Tunneling. Zbl 0626.35070
Simon, Barry
1984
Semiclassical analysis of low lying eigenvalues. I: Non-degenerate minima: Asymptotic expansions. Zbl 0526.35027
Simon, Barry
1983
Methods of modern mathematical physics. Vol. 3. Scattering theory. (Metody sovremennoj matematicheskoj fiziki. Tom 3. Teoriya rasseyaniya). Transl. from the English. Zbl 0517.47006
Reed, M.; Simon, B.
1982
The analytic theory of matrix orthogonal polynomials. Zbl 1193.42097
Damanik, David; Pushnitski, Alexander; Simon, Barry
2008
Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators. Zbl 0912.34074
Kiselev, Alexander; Last, Yoram; Simon, Barry
1998
Spectral analysis of rank one perturbations and applications. Zbl 0824.47019
Simon, Barry
1995
Almost periodic Schrödinger operators: A review. Zbl 0545.34023
Simon, Barry
1982
Functional integration and quantum physics. 2nd ed. Zbl 1061.28010
Simon, Barry
2005
Kotani theory for one dimensional stochastic Jacobi matrices. Zbl 0534.60057
Simon, Barry
1983
Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case. Zbl 0455.35112
Klaus, M.; Simon, Barry
1980
Representations of finite and compact groups. Zbl 0840.22001
Simon, Barry
1996
The classical limit of quantum partition functions. Zbl 0436.22012
Simon, Barry
1980
CMV matrices: Five years after. Zbl 1125.15027
Simon, Barry
2007
Phase space analysis of simple scattering systems: extensions of some work of Enss. Zbl 0402.35076
Simon, Barry
1979
Weakly coupled bound states in quantum waveguides. Zbl 0868.35080
Bulla, W.; Gesztesy, F.; Renger, W.; Simon, B.
1997
Scattering theory for systems with different spatial asymptotics on the left and right. Zbl 0393.34015
Davies, E. B.; Simon, B.
1978
Almost periodic Schrödinger operators. III: The absolutely continuous spectrum in one dimension. Zbl 0562.35026
Deift, P.; Simon, B.
1983
Maximal and minimal Schrödinger forms. Zbl 0446.35035
Simon, Barry
1979
Cantor spectrum for the almost Mathieu equation. Zbl 0516.47018
Bellissard, J.; Simon, B.
1982
The Birman-Krein-Vishik theory of self-adjoint extensions of semibounded operators. Zbl 0467.47017
Alonso, Alberto; Simon, Barry
1980
Singular continuous spectrum for palindromic Schrödinger operators. Zbl 0839.11009
Hof, A.; Knill, Oliver; Simon, Barry
1995
Almost periodic Schrödinger operators. I: Limit periodic potentials. Zbl 0484.35069
Avron, Joseph; Simon, Barry
1981
Subharmonicity of the Lyapunov index. Zbl 0518.35027
Craig, W.; Simon, B.
1983
Large time behavior of the $$L^ p$$ norm of Schrödinger semigroups. Zbl 0478.47024
Simon, Barry
1981
A new approach to inverse spectral theory. I: Fundamental formalism. Zbl 0945.34013
Simon, Barry
1999
Comparison theorems for the gap of Schrödinger operators. Zbl 0661.35062
Kirsch, Werner; Simon, Barry
1987
Schrödinger operators with magnetic fields. III: Atoms in homogeneous magnetic field. Zbl 0464.35086
Avron, J. E.; Herbst, I. W.; Simon, B.
1981
Perturbations of orthogonal polynomials with periodic recursion coefficients. Zbl 1194.47031
Damanik, David; Killip, Rowan; Simon, Barry
2010
On the measure of the spectrum for the almost Mathieu operator. Zbl 0724.47002
Avron, J.; von Mouche, P. H. M.; Simon, B.
1990
Operators with singular continuous spectrum. I: General operators. Zbl 0851.47003
Simon, Barry
1995
Operators with singular continuous spectrum. III: Almost periodic Schrödinger operators. Zbl 0830.34074
Jitomirskaya, Svetlana Ya.; Simon, Barry
1994
Resonances in one dimension and Fredholm determinants. Zbl 0977.34075
Simon, Barry
2000
A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure. Zbl 0983.34013
Gesztesy, Fritz; Simon, Barry
2000
Localization in general one-dimensional random systems. II: Continuum Schrödinger operators. Zbl 0637.60080
Kotani, S.; Simon, B.
1987
On positive eigenvalues of one body Schrödinger operators. Zbl 0167.11003
Simon, B.
1969
$$m$$-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices. Zbl 0924.15005
Gesztesy, Fritz; Simon, Barry
1997
Charge deficiency, charge transport and comparison of dimensions. Zbl 0822.47056
Avron, Joseph E.; Seiler, Ruedi; Simon, Barry
1994
Some quantum operators with discrete spectrum but classically continuous spectrum. Zbl 0547.35039
Simon, Barry
1983
Nonclassical eigenvalue asymptotics. Zbl 0529.35064
Simon, Barry
1983
Brownian motion, $$L^p$$ properties of Schrödinger operators and the localization of binding. Zbl 0446.47041
Simon, Barry
1980
Convexity. An analytic viewpoint. Zbl 1229.26003
Simon, Barry
2011
The essential spectrum of Schrödinger, Jacobi, and CMV operators. Zbl 1145.34052
Last, Yoram; Simon, Barry
2006
Distributions and their Hermite expansions. Zbl 0205.12901
Simon, B.
1971
Schrödinger operators in the twentieth century. Zbl 0981.81025
Simon, Barry
2000
Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices. Zbl 0532.60057
Craig, Walter; Simon, Barry
1983
Separation of center of mass in homogeneous magnetic fields. Zbl 0409.35027
Avron, J. E.; Herbst, I. W.; Simon, B.
1978
Equilibrium measures and capacities in spectral theory. Zbl 1149.31004
Simon, Barry
2007
Trace class perturbations and the absence of absolutely continuous spectra. Zbl 0684.47010
Simon, Barry; Spencer, Thomas
1989
Essential self-adjointness of Schrödinger operators with positive potentials. Zbl 0234.47027
Simon, Barry
1973
The $$\xi$$ function. Zbl 0885.34070
Gesztesy, Fritz; Simon, Barry
1996
Two extensions of Lubinsky’s universality theorem. Zbl 1168.42304
Simon, Barry
2008
Operators with singular continuous spectrum. II: Rank one operators. Zbl 1055.47500
del Río Castillo, Rafael René; Makarov, Nikolai G.; Simon, Barry
1994
Geometric methods in multiparticle quantum systems. Zbl 0413.47008
Simon, Barry
1977
The mathematical theory of resonances whose widths are exponentially small. Zbl 0455.35091
Harrell, E.; Simon, B.
1980
Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. IV. Zbl 0419.35079
Deift, P.; Hunziker, W.; Simon, B.; Vock, E.
1978
An abstract Kato’s inequality for generators of positivity preserving semigroups. Zbl 0389.47021
Simon, Barry
1977
On the decoupling of finite singularities from the question of asymptotic completeness in two body quantum systems. Zbl 0344.47007
Deift, P.; Simon, B.
1976
The Christoffel-Darboux kernel. Zbl 1159.42020
Simon, Barry
2008
OPUC on one foot. Zbl 1108.42005
Simon, Barry
2005
Rank one perturbations at infinite coupling. Zbl 0828.47009
Gesztesy, Fritz; Simon, Barry
1995
The essential spectrum of Neumann Laplacians on some bounded singular domains. Zbl 0741.35043
Hempel, Rainer; Seco, Luis A.; Simon, Barry
1991
$$L^ p$$ norms of non-critical Schrödinger semigroups. Zbl 0743.47047
Davies, E. B.; Simon, B.
1991
Singular continuous spectrum for a class of almost periodic Jacobi matrices. Zbl 0491.47014
Avron, Joseph; Simon, Barry
1982
Harmonic analysis on SL(2,R) and smoothness of the density of states in the one-dimensional Anderson model. Zbl 0577.60067
Simon, Barry; Taylor, Michael
1985
Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. V: Lower bounds and path integrals. Zbl 0464.35085
Carmona, R.; Simon, B.
1981
Asymptotics of Chebyshev polynomials. III: Sets saturating Szegő, Schiefermayr, and Totik-Widom bounds. Zbl 1448.41026
Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
2020
Asymptotics of Chebyshev polynomials. II: DCT subsets of $$\mathbb{R}$$. Zbl 1426.41035
Christiansen, Jacob S.; Simon, Barry; Yuditskii, Peter; Zinchenko, Maxim
2019
Loewner’s theorem on monotone matrix functions. Zbl 1428.26002
Simon, Barry
2019
Poncelet’s theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators. Zbl 07060783
Martínez-Finkelshtein, Andrei; Simanek, Brian; Simon, Barry
2019
Large deviations and the Lukic conjecture. Zbl 1426.60032
Breuer, Jonathan; Simon, Barry; Zeitouni, Ofer
2018
Large deviations and sum rules for spectral theory: a pedagogical approach. Zbl 1402.60029
Breuer, Jonathan; Simon, Barry; Zeitouni, Ofer
2018
Tosio Kato’s work on non-relativistic quantum mechanics. I. Zbl 1416.81063
Simon, Barry
2018
Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061
Frank, Rupert L.; Simon, Barry
2017
Asymptotics of Chebyshev polynomials. I: Subsets of $${\mathbb {R}}$$. Zbl 1369.41031
Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
2017
Unitaries permuting two orthogonal projections. Zbl 06950136
Simon, Barry
2017
Similarity between two projections. Zbl 06832763
Böttcher, Albrecht; Simon, Barry; Spitkovsky, Ilya
2017
A Cayley-Hamiltonian theorem for periodic finite band matrices. Zbl 1376.15008
Simon, Barry
2017
Condensation of fermion pairs in a domain. Zbl 1372.82044
Frank, Rupert L.; Lemm, Marius; Simon, Barry
2017
Operator theory. A comprehensive course in analysis, part 4. Zbl 1334.00003
Simon, Barry
2015
Basic complex analysis. A comprehensive course in analysis, part 2A. Zbl 1332.00004
Simon, Barry
2015
Harmonic analysis. A comprehensive course in analysis, part 3. Zbl 1334.00002
Simon, Barry
2015
Real analysis. A comprehensive course in analysis, part 1. Zbl 1332.00003
Simon, Barry
2015
Cantor polynomials and some related classes of OPRL. Zbl 1309.42034
Krüger, Helge; Simon, Barry
2015
Advanced complex analysis. A comprehensive course in analysis, part 2B. Zbl 1332.00005
Simon, Barry
2015
Stability of asymptotics of Christoffel-Darboux kernels. Zbl 1412.60053
Breuer, Jonathan; Last, Yoram; Simon, Barry
2014
Spectral theory of orthogonal polynomials. Zbl 1301.31003
Simon, B.
2014
Finite gap Jacobi matrices: a review. Zbl 1319.47028
Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
2013
Finite gap Jacobi matrices. III: Beyond the Szegő class. Zbl 1238.42009
Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
2012
Szegő’s theorem and its descendants. Spectral theory for $$L^2$$ perturbations of orthogonal polynomials. Zbl 1230.33001
Simon, Barry
2011
Convexity. An analytic viewpoint. Zbl 1229.26003
Simon, Barry
2011
Finite gap Jacobi matrices. II: The Szegő class. Zbl 1236.42021
Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
2011
Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Zbl 1229.35157
Frank, Rupert L.; Simon, Barry
2011
Natural boundaries and spectral theory. Zbl 1219.30001
Breuer, Jonathan; Simon, Barry
2011
Asymptotics of the $$L^2$$ norm of derivatives of OPUC. Zbl 1220.42019
Martínez-Finkelshtein, Andrei; Simon, Barry
2011
On the removal of finite discrete spectrum by coefficient stripping. Zbl 1277.47046
Simon, Barry
2011
Perturbations of orthogonal polynomials with periodic recursion coefficients. Zbl 1194.47031
Damanik, David; Killip, Rowan; Simon, Barry
2010
Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum. Zbl 1225.26031
Avila, Artur; Last, Yoram; Simon, Barry
2010
Finite gap Jacobi matrices. I: The isospectral torus. Zbl 1200.42012
Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
2010
Equality of the spectral and dynamical definitions of reflection. Zbl 1190.47032
Breuer, Jonathan; Ryckman, Eric; Simon, Barry
2010
The Nevai condition. Zbl 1198.42021
Breuer, Jonathan; Last, Yoram; Simon, Barry
2010
The Hilbert transform of a measure. Zbl 1211.30052
Poltoratski, Alexei; Simon, Barry; Zinchenko, Maxim
2010
Weak convergence of CD kernels and applications. Zbl 1158.33003
Simon, Barry
2009
Sum rules and spectral measures of Schrödinger operators with $$L^2$$ potentials. Zbl 1185.34131
Killip, Rowan; Simon, Barry
2009
Schrödinger operators with purely discrete spectrum. Zbl 1199.47198
Simon, Barry
2009
Regularity and the Cesàro-Nevai class. Zbl 1167.42010
Simon, Barry
2009
Finite gap Jacobi matrices: An announcement. Zbl 1174.42028
Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
2009
Monotone Jacobi parameters and non-Szegő weights. Zbl 1185.42027
Kreimer, Yury; Last, Yoram; Simon, Barry
2009
Poisson brackets of orthogonal polynomials. Zbl 1200.41040
Cantero, María José; Simon, Barry
2009
A celebration of Jürg and Tom. Zbl 1166.82300
Simon, Barry
2009
The analytic theory of matrix orthogonal polynomials. Zbl 1193.42097
Damanik, David; Pushnitski, Alexander; Simon, Barry
2008
Two extensions of Lubinsky’s universality theorem. Zbl 1168.42304
Simon, Barry
2008
The Christoffel-Darboux kernel. Zbl 1159.42020
Simon, Barry
2008
Fine structure of the zeros of orthogonal polynomials. IV: A priori bounds and clock behavior. Zbl 1214.42044
Last, Yoram; Simon, Barry
2008
On the Koplienko spectral shift function. I: Basics. Zbl 1190.47016
Gesztesy, F.; Pushnitski, A.; Simon, B.
2008
Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states. Zbl 1158.35021
Frank, Rupert L.; Simon, Barry; Weidl, Timo
2008
Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices. Zbl 1135.47026
Hundertmark, Dirk; Simon, Barry
2008
CMV matrices: Five years after. Zbl 1125.15027
Simon, Barry
2007
Equilibrium measures and capacities in spectral theory. Zbl 1149.31004
Simon, Barry
2007
Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle. Zbl 1110.33004
Simon, Barry
2007
Orthogonal polynomials with exponentially decaying recursion coefficients. Zbl 1143.42306
Simon, Barry
2007
Zeros of OPUC and long time asymptotics of Schur and related flows. Zbl 1125.35098
Simon, Barry
2007
Meromorphic Jost functions and asymptotic expansions for Jacobi parameters. Zbl 1255.47031
Simon, Barry
2007
The essential spectrum of Schrödinger, Jacobi, and CMV operators. Zbl 1145.34052
Last, Yoram; Simon, Barry
2006
Fine structure of the zeros of orthogonal polynomials. I: A tale of two pictures. Zbl 1129.42011
Simon, Barry
2006
Jost functions and Jost solutions for Jacobi matrices. I: A necessary and sufficient condition for Szegő asymptotics. Zbl 1122.47029
Damanik, David; Simon, Barry
2006
Jost functions and Jost solutions for Jacobi matrices. II: Decay and analyticity. Zbl 1122.47030
Damanik, David; Simon, Barry
2006
Aizenman’s theorem for orthogonal polynomials on the unit circle. Zbl 1104.42014
Simon, Barry
2006
Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle. Zbl 1127.47037
Davies, E. B.; Simon, B.
2006
Fine structure of the zeros of orthogonal polynomials. III: Periodic recursion coefficients. Zbl 1129.42013
Simon, Barry
2006
Trace ideals and their applications. 2nd ed. Zbl 1074.47001
Simon, Barry
2005
Orthogonal polynomials on the unit circle. Part 1: Classical theory. Zbl 1082.42020
Simon, Barry
2005
Orthogonal polynomials on the unit circle. Part 2: Spectral theory. Zbl 1082.42021
Simon, Barry
2005
Functional integration and quantum physics. 2nd ed. Zbl 1061.28010
Simon, Barry
2005
OPUC on one foot. Zbl 1108.42005
Simon, Barry
2005
Sturm oscillation and comparison theorems. Zbl 1117.39013
Simon, Barry
2005
Schrödinger operators with few bound states. Zbl 1082.47029
Damanik, David; Killip, Rowan; Simon, Barry
2005
On a theorem of Kac and Gilbert. Zbl 1071.47027
Simon, Barry
2005
Higher-order Szegő theorems with two singular points. Zbl 1067.30075
Simon, Barry; Zlatoš, Andrej
2005
Fine structure of the zeros of orthogonal polynomials. II: OPUC with competing exponential decay. Zbl 1129.42012
Simon, Barry
2005
Meromorphic Szegő functions and asymptotic series for Verblunsky coefficients. Zbl 1117.42005
Simon, Barry
2005
The sharp form of the strong Szegő theorem. Zbl 1093.47032
Simon, Barry
2005
Limits of zeros of orthogonal polynomials on the circle. Zbl 1077.42017
Simon, Barry; Totik, Vilmos
2005
Orthogonal polynomials on the unit circle: new results. Zbl 1086.42501
Simon, Barry
2004
A diamagnetic inequality for semigroup differences. Zbl 1068.47052
Hundertmark, Dirk; Simon, Barry
2004
Analogs of the $$m$$-function in the theory of orthogonal polynomials on the unit circle. Zbl 1055.33010
Simon, Barry
2004
A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices. Zbl 1064.30030
Simon, Barry
2004
Ratio asymptotics and weak asymptotic measures for orthogonal polynomials on the real line. Zbl 1043.42017
Simon, Barry
2004
Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators. Zbl 1084.34075
Damanik, David; Killip, Rowan; Simon, Barry
2004
Connectedness of the isospectral manifold for one-dimensional half-line Schrödinger operators. Zbl 1138.81019
Gesztesy, Fritz; Simon, Barry
2004
Sum rules for Jacobi matrices and their applications to spectral theory. Zbl 1050.47025
Killip, Rowan; Simon, Barry
2003
Sum rules and the Szegő condition for orthogonal polynomials on the real line. Zbl 1046.42017
Simon, Barry; Zlatoš, Andrej
2003
Variational estimates for discrete Schrödinger operators with potentials of indefinite sign. Zbl 1052.47027
Damanik, D.; Hundertmark, D.; Killip, R.; Simon, B.
2003
Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators. Zbl 1049.47032
Damanik, David; Hundertmark, Dirk; Simon, Barry
2003
Stability of singular spectral types under decaying perturbations. Zbl 1029.34073
Kiselev, Alexander; Last, Yoram; Simon, Barry
2003
Zeros of orthogonal polynomials on the real line. Zbl 1031.42022
Denisov, Sergey A.; Simon, Barry
2003
The Golinskii-Ibragimov method and a theorem of Damanik and Killip. Zbl 1042.42019
Simon, Barry
2003
Lieb-Thirring inequalities for Jacobi matrices. Zbl 1019.39013
Hundertmark, Dirk; Simon, Barry
2002
An optimal $$L^p$$-bound on the Krein spectral shift function. Zbl 1054.47020
Hundertmark, Dirk; Simon, Barry
2002
Approach to equilibrium for a forced Burgers equation. Zbl 0996.35010
Kirsch, Werner; Simon, Barry
2001
Inverse spectral analysis with partial information on the potential. II: The case of discrete spectrum. Zbl 0948.34060
Gesztesy, Fritz; Simon, Barry
2000
Resonances in one dimension and Fredholm determinants. Zbl 0977.34075
Simon, Barry
2000
A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure. Zbl 0983.34013
Gesztesy, Fritz; Simon, Barry
2000
Schrödinger operators in the twentieth century. Zbl 0981.81025
Simon, Barry
2000
Schrödinger operators in the twenty-first century. Zbl 1074.81521
Simon, Barry
2000
On local Borg-Marchenko uniqueness results. Zbl 0985.34077
Gesztesy, Fritz; Simon, Barry
2000
...and 227 more Documents
all top 5

#### Cited by 9,095 Authors

 191 Simon, Barry 114 Albeverio, Sergio A. 103 Gesztesy, Fritz 74 Damanik, David 60 Exner, Pavel 55 Davies, Edward Brian 54 Helffer, Bernard 53 Fröhlich, Jürg Martin 50 Sukochev, Fedor Anatol’evich 47 Sigal, Israel Michael 43 Arai, Asao 43 Frank, Rupert L. 41 Lewin, Mathieu 41 Lieb, Elliott H. 40 Klein, Abel 39 Jitomirskaya, Svetlana Ya. 39 Korotyaev, Evgeny L. 38 Herbst, Ira W. 37 Gérard, Christian 37 Yang, Chuanfu 34 Solovej, Jan Philip 33 Stolz, Gunter 32 Kirsch, Werner 32 Marcellán Español, Francisco 31 Ding, Yanheng 31 Lenz, Daniel H. 31 Lubinsky, Doron S. 31 Raikov, Georgi D. 31 Song, Renming 29 Chen, Zhen-Qing 29 Fournais, Søren 29 Hiroshima, Fumio 29 Wei, Guangsheng 28 Last, Yoram 27 Borisov, Denis Ivanovich 27 Jakšić, Vojkan 27 Nakamura, Shu 27 Röckner, Michael 26 de Oliveira, César R. 26 Klopp, Frédéric 26 Seiringer, Robert 26 Sobolev, Alexander V. 26 Weinstein, Michael I. 25 Harrell, Evans M. II 25 Kittaneh, Fuad 25 Naboko, Serguei N. 25 Neidhardt, Hagen 25 Schulz-Baldes, Hermann 25 Siedentop, Heinz Karl Heinrich 25 Weder, Ricardo A. 25 Yafaev, Dimitri R. 24 Carey, Alan L. 24 Jørgensen, Palle E. T. 24 Tamura, Hideo 24 Teschl, Gerald 23 Kondrat’yev, Yuriĭ Grygorovych 23 Krejčiřík, David 23 Nazarov, Sergeĭ Aleksandrovich 23 Zinchenko, Maxim 22 Briet, Philippe 22 Hislop, Peter D. 22 Ichinose, Takashi 22 Jensen, Arne 22 Molchanov, Stanislav Alekseevich 22 Pillet, Claude-Alain 22 Pushnitski, Alexander B. 22 Skibsted, Erik 21 Behrndt, Jussi 21 Breuer, Jonathan 21 Combes, Jean-Michel 21 Demuth, Michael 21 Denisov, Sergey A. 21 Gadella, Manuel 21 Lakaev, Saidakhmat Norzhigitovich 21 Pinchover, Yehuda 21 Spohn, Herbert 21 Veselić, Ivan 21 Zagrebnov, Valentin A. 21 Zhao, Zhongxin 20 Avron, Joseph E. 20 Cancès, Eric 20 Fillman, Jake 20 Hainzl, Christian 20 Hoffmann-Ostenhof, Thomas 20 Joye, Alain 20 Kovařík, Hynek 20 Martinez, André 20 Nenciu, Gheorghe 20 Wang, Feng-Yu 20 Wang, Xueping 19 Bach, Volker 19 Boutet de Monvel, Anne Marie 19 Deift, Percy A. 19 Hoffmann-Ostenhof, Maria 19 Holden, Helge 19 Klaus, Martin 19 Laptev, Ari 19 Lebowitz, Joel Louis 19 Lotoreichik, Vladimir 19 Malamud, Mark M. ...and 8,995 more Authors
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#### Cited in 629 Serials

 954 Communications in Mathematical Physics 815 Journal of Functional Analysis 726 Journal of Mathematical Physics 444 Journal of Mathematical Analysis and Applications 289 Journal of Statistical Physics 266 Journal of Differential Equations 224 Annales Henri Poincaré 213 Letters in Mathematical Physics 200 Proceedings of the American Mathematical Society 183 Reviews in Mathematical Physics 177 Theoretical and Mathematical Physics 168 Communications in Partial Differential Equations 167 Transactions of the American Mathematical Society 158 Integral Equations and Operator Theory 157 Annales de l’Institut Henri Poincaré. Physique Théorique 140 Reports on Mathematical Physics 136 Linear Algebra and its Applications 130 Advances in Mathematics 123 Journal of Approximation Theory 113 Annals of Physics 105 Duke Mathematical Journal 100 Journal of Mathematical Sciences (New York) 98 Mathematische Zeitschrift 90 Journal d’Analyse Mathématique 89 Archive for Rational Mechanics and Analysis 87 Mathematische Nachrichten 76 Mathematical Notes 74 Physics Letters. A 74 Mathematische Annalen 72 Journal of Geometry and Physics 72 Functional Analysis and its Applications 71 Publications of the Research Institute for Mathematical Sciences, Kyoto University 68 Journal of Computational and Applied Mathematics 68 Probability Theory and Related Fields 66 Potential Analysis 64 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 64 Stochastic Processes and their Applications 62 Mathematical Physics, Analysis and Geometry 62 Journal of Spectral Theory 61 The Annals of Probability 59 Journal de Mathématiques Pures et Appliquées. Neuvième Série 56 Communications on Pure and Applied Mathematics 54 International Journal of Theoretical Physics 54 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 53 Physica D 52 Annales de l’Institut Fourier 50 SIAM Journal on Mathematical Analysis 50 Comptes Rendus. Mathématique. Académie des Sciences, Paris 49 Ukrainian Mathematical Journal 49 Complex Analysis and Operator Theory 48 Infinite Dimensional Analysis, Quantum Probability and Related Topics 47 Constructive Approximation 45 Journal of Soviet Mathematics 45 Calculus of Variations and Partial Differential Equations 43 Inventiones Mathematicae 42 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 41 Acta Applicandae Mathematicae 39 Applicable Analysis 39 Mathematical Methods in the Applied Sciences 39 Nuclear Physics. B 38 Applied Mathematics and Computation 38 Bulletin of the American Mathematical Society. New Series 38 Journal of Pseudo-Differential Operators and Applications 35 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 35 Nonlinear Analysis. Theory, Methods & Applications 34 Russian Journal of Mathematical Physics 34 St. Petersburg Mathematical Journal 32 The Journal of Geometric Analysis 31 Israel Journal of Mathematics 31 Discrete and Continuous Dynamical Systems 30 Journal of Computational Physics 30 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 29 Applied Mathematics Letters 29 Journal of the American Mathematical Society 29 Doklady Mathematics 28 Arkiv för Matematik 28 Ergodic Theory and Dynamical Systems 28 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 27 Manuscripta Mathematica 27 The Annals of Applied Probability 27 Journal of Dynamics and Differential Equations 27 Positivity 26 Monatshefte für Mathematik 25 Annali di Matematica Pura ed Applicata. Serie Quarta 25 Memoirs of the American Mathematical Society 25 Advances in Applied Mathematics 25 The Journal of Fourier Analysis and Applications 25 Journal of the European Mathematical Society (JEMS) 24 Rocky Mountain Journal of Mathematics 24 Acta Mathematica 24 Journal of Physics A: Mathematical and Theoretical 23 ZAMP. Zeitschrift für angewandte Mathematik und Physik 23 Journal of Theoretical Probability 23 Geometric and Functional Analysis. GAFA 22 Computers & Mathematics with Applications 22 Transport Theory and Statistical Physics 22 Mathematics of Computation 22 Siberian Mathematical Journal 22 Bulletin des Sciences Mathématiques 22 Journal of High Energy Physics ...and 529 more Serials
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#### Cited in 62 Fields

 4,336 Partial differential equations (35-XX) 3,949 Quantum theory (81-XX) 3,792 Operator theory (47-XX) 1,520 Probability theory and stochastic processes (60-XX) 1,351 Statistical mechanics, structure of matter (82-XX) 1,193 Functional analysis (46-XX) 1,064 Ordinary differential equations (34-XX) 807 Global analysis, analysis on manifolds (58-XX) 602 Harmonic analysis on Euclidean spaces (42-XX) 560 Dynamical systems and ergodic theory (37-XX) 356 Linear and multilinear algebra; matrix theory (15-XX) 347 Numerical analysis (65-XX) 291 Special functions (33-XX) 288 Differential geometry (53-XX) 278 Functions of a complex variable (30-XX) 260 Fluid mechanics (76-XX) 246 Optics, electromagnetic theory (78-XX) 221 Difference and functional equations (39-XX) 200 Measure and integration (28-XX) 194 Relativity and gravitational theory (83-XX) 177 Calculus of variations and optimal control; optimization (49-XX) 170 Potential theory (31-XX) 169 Mechanics of particles and systems (70-XX) 167 Topological groups, Lie groups (22-XX) 154 Approximations and expansions (41-XX) 147 Combinatorics (05-XX) 120 Real functions (26-XX) 116 Integral equations (45-XX) 107 Number theory (11-XX) 107 Abstract harmonic analysis (43-XX) 104 Statistics (62-XX) 104 Mechanics of deformable solids (74-XX) 99 Integral transforms, operational calculus (44-XX) 94 Information and communication theory, circuits (94-XX) 90 Systems theory; control (93-XX) 77 Several complex variables and analytic spaces (32-XX) 67 Biology and other natural sciences (92-XX) 66 Computer science (68-XX) 60 Algebraic geometry (14-XX) 60 Group theory and generalizations (20-XX) 47 Manifolds and cell complexes (57-XX) 47 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 41 Nonassociative rings and algebras (17-XX) 39 $$K$$-theory (19-XX) 35 Mathematical logic and foundations (03-XX) 35 Classical thermodynamics, heat transfer (80-XX) 34 Convex and discrete geometry (52-XX) 30 Sequences, series, summability (40-XX) 29 Astronomy and astrophysics (85-XX) 28 Operations research, mathematical programming (90-XX) 23 Associative rings and algebras (16-XX) 18 Algebraic topology (55-XX) 16 Category theory; homological algebra (18-XX) 15 General and overarching topics; collections (00-XX) 14 History and biography (01-XX) 12 General topology (54-XX) 11 Order, lattices, ordered algebraic structures (06-XX) 11 Geometry (51-XX) 9 Geophysics (86-XX) 5 Commutative algebra (13-XX) 4 Field theory and polynomials (12-XX) 1

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