# zbMATH — the first resource for mathematics

## Simon, Barry

Compute Distance To:
 Author ID: simon.barry.1 Published as: Simon, Barry; Simon, B.; Simon Homepage: http://math.caltech.edu/simon/simon.html External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef
 Documents Indexed: 361 Publications since 1968, including 34 Books Biographic References: 7 Publications
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#### Co-Authors

 151 single-authored 32 Gesztesy, Fritz 16 Avron, Joseph E. 12 Last, Yoram 11 Zinchenko, Maxim 10 Christiansen, Jacob Stordal 10 Reed, Michael C. 9 Davies, Edward Brian 9 Holden, Helge 8 Damanik, David 8 Kirsch, Werner 7 Breuer, Jonathan 7 del Río Castillo, Rafael René 6 Hundertmark, Dirk 6 Killip, Rowan 5 Frank, Rupert L. 5 Jitomirskaya, Svetlana Yakovlevna 4 Deift, Percy A. 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 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 Belibassakis, Konstadinos A. 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 Jensen, Arne 1 Knill, Oliver 1 Kraenkel, Roberto A. 1 Kreimer, Yury 1 Kriegseis, Jochen 1 Krüger, Helge 1 Kuhnhenn, M. 1 Kuroda, Shige Toshi 1 Lemm, Marius 1 Maden, I. 1 Manna, Miguel A. 1 Masters, Wen Chen 1 Merz, Konstantin 1 Miller, Keith D. 1 Nappi, Chiara R. ...and 37 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 Journal d’Analyse Mathématique 9 Annals of Mathematics. Second Series 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 Mathematical Physics 4 Journal of Spectral Theory 4 Princeton Series in Physics 3 American Mathematical Monthly 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 Wave Motion 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 2 Bulletin of Mathematical Sciences 1 Archive for Rational Mechanics and Analysis 1 Helvetica Physica Acta 1 Journal of Fluid Mechanics 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 Pure and Applied Functional Analysis 1 Operator Theory: Advances and Applications
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#### Fields

 165 Operator theory (47-XX) 118 Partial differential equations (35-XX) 91 Quantum theory (81-XX) 68 Ordinary differential equations (34-XX) 48 Harmonic analysis on Euclidean spaces (42-XX) 36 Functional analysis (46-XX) 36 Probability theory and stochastic processes (60-XX) 26 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) 7 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) 5 Fluid mechanics (76-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) 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 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

330 Publications have been cited 18,617 times in 11,563 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. I: Functional analysis. Rev. and enl. ed. Zbl 0459.46001
Reed, Michael; Simon, Barry
1980
Methods of modern mathematical physics. 1: Functional analysis. Zbl 0242.46001
Reed, Michael; Simon, Barry
1972
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
Schrödinger operators with magnetic fields. I: General interactions. Zbl 0399.35029
Avron, J.; Herbst, I.; Simon, B.
1978
The $$P(\phi )_{2}$$ Euclidean (quantum) field theory. Zbl 1175.81146
Simon, Barry
1974
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
Spectral analysis of N-body Schrödinger operators. Zbl 0477.35069
Perry, P.; Sigal, I. M.; Simon, B.
1981
Quantum mechanics for Hamiltonians defined as quadratic forms. Zbl 0232.47053
Simon, Barry
1971
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
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 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
Szegő’s theorem and its descendants. Spectral theory for $$L^2$$ perturbations of orthogonal polynomials. Zbl 1230.33001
Simon, Barry
2011
Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions. Zbl 0716.35006
Carmona, René; Masters, Wen Chen; Simon, Barry
1990
Hypercontra ctive semigroups and two dimensional self-coupled Bose fields. Zbl 0241.47029
Simon, Barry; Høegh-Krohn, Raphael
1972
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 index of a pair of projections. Zbl 0822.47033
Avron, Joseph E.; Seiler, Ruedi; Simon, Barry
1994
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
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
The analytic theory of matrix orthogonal polynomials. Zbl 1193.42097
Damanik, David; Pushnitski, Alexander; Simon, Barry
2008
The statistical mechanics of lattice gases. Vol. I. Zbl 0804.60093
Simon, Barry
1993
Functional integration and quantum physics. 2nd ed. Zbl 1061.28010
Simon, Barry
2005
Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators. Zbl 0912.34074
Kiselev, Alexander; Last, Yoram; Simon, Barry
1998
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
Almost periodic Schrödinger operators: A review. Zbl 0545.34023
Simon, Barry
1982
Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case. Zbl 0455.35112
Klaus, M.; Simon, Barry
1980
Spectral analysis of rank one perturbations and applications. Zbl 0824.47019
Simon, Barry
1995
Kotani theory for one dimensional stochastic Jacobi matrices. Zbl 0534.60057
Simon, Barry
1983
The classical limit of quantum partition functions. Zbl 0436.22012
Simon, Barry
1980
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
Phase space analysis of simple scattering systems: extensions of some work of Enss. Zbl 0402.35076
Simon, Barry
1979
CMV matrices: Five years after. Zbl 1125.15027
Simon, Barry
2007
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
Singular continuous spectrum for palindromic Schrödinger operators. Zbl 0839.11009
Hof, A.; Knill, Oliver; Simon, Barry
1995
Representations of finite and compact groups. Zbl 0840.22001
Simon, Barry
1996
Almost periodic Schrödinger operators. I: Limit periodic potentials. Zbl 0484.35069
Avron, Joseph; Simon, Barry
1981
The Birman-Krein-Vishik theory of self-adjoint extensions of semibounded operators. Zbl 0467.47017
Alonso, Alberto; Simon, Barry
1980
A new approach to inverse spectral theory. I: Fundamental formalism. Zbl 0945.34013
Simon, Barry
1999
Large time behavior of the $$L^ p$$ norm of Schrödinger semigroups. Zbl 0478.47024
Simon, Barry
1981
Schrödinger operators with magnetic fields. III: Atoms in homogeneous magnetic field. Zbl 0464.35086
Avron, J. E.; Herbst, I. W.; Simon, B.
1981
Operators with singular continuous spectrum. I: General operators. Zbl 0851.47003
Simon, Barry
1995
Subharmonicity of the Lyapunov index. Zbl 0518.35027
Craig, W.; Simon, B.
1983
Perturbations of orthogonal polynomials with periodic recursion coefficients. Zbl 1194.47031
Damanik, David; Killip, Rowan; Simon, Barry
2010
Comparison theorems for the gap of Schrödinger operators. Zbl 0661.35062
Kirsch, Werner; Simon, Barry
1987
Operators with singular continuous spectrum. III: Almost periodic Schrödinger operators. Zbl 0830.34074
Jitomirskaya, Svetlana Ya.; Simon, Barry
1994
On the measure of the spectrum for the almost Mathieu operator. Zbl 0724.47002
Avron, J.; von Mouche, P. H. M.; Simon, B.
1990
$$m$$-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices. Zbl 0924.15005
Gesztesy, Fritz; Simon, Barry
1997
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
Charge deficiency, charge transport and comparison of dimensions. Zbl 0822.47056
Avron, Joseph E.; Seiler, Ruedi; Simon, Barry
1994
On positive eigenvalues of one body Schrödinger operators. Zbl 0167.11003
Simon, B.
1969
Localization in general one-dimensional random systems. II: Continuum Schrödinger operators. Zbl 0637.60080
Kotani, S.; Simon, B.
1987
Operator theory. A comprehensive course in analysis, part 4. Zbl 1334.00003
Simon, Barry
2015
Some quantum operators with discrete spectrum but classically continuous spectrum. Zbl 0547.35039
Simon, Barry
1983
Convexity. An analytic viewpoint. Zbl 1229.26003
Simon, Barry
2011
Distributions and their Hermite expansions. Zbl 0205.12901
Simon, B.
1971
Resonances in one dimension and Fredholm determinants. Zbl 0977.34075
Simon, Barry
2000
The essential spectrum of Schrödinger, Jacobi, and CMV operators. Zbl 1145.34052
Last, Yoram; Simon, Barry
2006
Separation of center of mass in homogeneous magnetic fields. Zbl 0409.35027
Avron, J. E.; Herbst, I. W.; Simon, B.
1978
Brownian motion, $$L^p$$ properties of Schrödinger operators and the localization of binding. Zbl 0446.47041
Simon, Barry
1980
Nonclassical eigenvalue asymptotics. Zbl 0529.35064
Simon, Barry
1983
Schrödinger operators in the twentieth century. Zbl 0981.81025
Simon, Barry
2000
Equilibrium measures and capacities in spectral theory. Zbl 1149.31004
Simon, Barry
2007
Essential self-adjointness of Schrödinger operators with positive potentials. Zbl 0234.47027
Simon, Barry
1973
Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices. Zbl 0532.60057
Craig, Walter; Simon, Barry
1983
The $$\xi$$ function. Zbl 0885.34070
Gesztesy, Fritz; Simon, Barry
1996
Operators with singular continuous spectrum. II: Rank one operators. Zbl 1055.47500
del Río Castillo, Rafael René; Makarov, Nikolai G.; Simon, Barry
1994
Two extensions of Lubinsky’s universality theorem. Zbl 1168.42304
Simon, Barry
2008
Geometric methods in multiparticle quantum systems. Zbl 0413.47008
Simon, Barry
1977
Trace class perturbations and the absence of absolutely continuous spectra. Zbl 0684.47010
Simon, Barry; Spencer, Thomas
1989
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
An abstract Kato’s inequality for generators of positivity preserving semigroups. Zbl 0389.47021
Simon, Barry
1977
The Christoffel-Darboux kernel. Zbl 1159.42020
Simon, Barry
2008
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
OPUC on one foot. Zbl 1108.42005
Simon, Barry
2005
The essential spectrum of Neumann Laplacians on some bounded singular domains. Zbl 0741.35043
Hempel, Rainer; Seco, Luis A.; Simon, Barry
1991
Rank one perturbations at infinite coupling. Zbl 0828.47009
Gesztesy, Fritz; Simon, Barry
1995
$$L^ p$$ 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
Unique continuation for Schrödinger operators with unbounded potentials. Zbl 0458.35024
Schechter, M.; Simon, B.
1980
Periodic Jacobi matrices on trees. Zbl 07212216
Avni, Nir; Breuer, Jonathan; Simon, Barry
2020
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. IV: Comments on the complex case. Zbl 1472.30001
Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
2020
Loewner’s theorem on monotone matrix functions. Zbl 1428.26002
Simon, Barry
2019
Asymptotics of Chebyshev polynomials. II: DCT subsets of $$\mathbb{R}$$. Zbl 1426.41035
Christiansen, Jacob S.; Simon, Barry; Yuditskii, Peter; Zinchenko, Maxim
2019
Poncelet’s theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators. Zbl 07060783
Martínez-Finkelshtein, Andrei; Simanek, Brian; Simon, Barry
2019
Tosio Kato’s work on non-relativistic quantum mechanics. II. Zbl 1472.81094
Simon, Barry
2019
Large deviations and sum rules for spectral theory: a pedagogical approach. Zbl 1402.60029
Breuer, Jonathan; Simon, Barry; Zeitouni, Ofer
2018
Large deviations and the Lukic conjecture. Zbl 1426.60032
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
A coupled-mode model for water wave scattering by vertically sheared currents in variable bathymetry regions. Zbl 07213191
Belibassakis, K. A.; Simon, B.; Touboul, J.; Rey, V.
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
Poisson brackets of orthogonal polynomials. Zbl 1200.41040
Cantero, María José; Simon, Barry
2009
Monotone Jacobi parameters and non-Szegő weights. Zbl 1185.42027
Kreimer, Yury; Last, Yoram; 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
Fine structure of the zeros of orthogonal polynomials: a review. Zbl 1214.42052
Simon, Barry
2007
The essential spectrum of Schrödinger, Jacobi, and CMV operators. Zbl 1145.34052
Last, Yoram; 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
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. 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
Higher-order Szegő theorems with two singular points. Zbl 1067.30075
Simon, Barry; Zlatoš, Andrej
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
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
Variational estimates for discrete Schrödinger operators with potentials of indefinite sign. Zbl 1052.47027
Damanik, D.; Hundertmark, D.; Killip, R.; Simon, B.
2003
Sum rules and the Szegő condition for orthogonal polynomials on the real line. Zbl 1046.42017
Simon, Barry; Zlatoš, Andrej
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
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
...and 230 more Documents
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#### Cited by 8,529 Authors

 189 Simon, Barry 108 Gesztesy, Fritz 102 Albeverio, Sergio A. 73 Damanik, David 61 Exner, Pavel 55 Helffer, Bernard 53 Davies, Edward Brian 49 Fröhlich, Jürg Martin 48 Sukochev, Fedor Anatol’evich 47 Sigal, Israel Michael 44 Frank, Rupert L. 44 Lewin, Mathieu 43 Arai, Asao 43 Korotyaev, Evgeny L. 42 Lieb, Elliott H. 41 Jitomirskaya, Svetlana Yakovlevna 41 Yang, Chuanfu 40 Klein, Abel 38 Herbst, Ira W. 36 Gérard, Christian 33 Solovej, Jan Philip 32 Ding, Yanheng 32 Stolz, Gunter 31 Lenz, Daniel H. 31 Raikov, Georgi D. 31 Seiringer, Robert 31 Song, Renming 30 de Oliveira, César R. 30 Fournais, Søren 30 Kirsch, Werner 30 Wei, Guangsheng 29 Chen, Zhen-Qing 29 Marcellán Español, Francisco 28 Borisov, Denis Ivanovich 28 Hiroshima, Fumio 28 Last, Yoram 28 Lubinsky, Doron S. 27 Jakšić, Vojkan 26 Klopp, Frédéric 26 Nazarov, Sergeĭ Aleksandrovich 26 Schulz-Baldes, Hermann 26 Zinchenko, Maxim 25 Kittaneh, Fuad 25 Naboko, Serguei N. 25 Sobolev, Alexander V. 25 Weder, Ricardo A. 25 Weinstein, Michael I. 24 Carey, Alan L. 24 Hislop, Peter D. 24 Siedentop, Heinz Karl Heinrich 24 Teschl, Gerald 23 Breuer, Jonathan 23 Fillman, Jake 23 Krejčiřík, David 23 Nakamura, Shu 23 Veselić, Ivan 23 Yafaev, Dimitri R. 22 Combes, Jean-Michel 22 Harrell, Evans M. II 22 Ichinose, Takashi 22 Jensen, Arne 22 Kondrat’yev, Yuriĭ Grygorovych 22 Pillet, Claude-Alain 22 Pushnitski, Alexander B. 22 Röckner, Michael 22 Skibsted, Erik 22 Tamura, Hideo 21 Demuth, Michael 21 Jørgensen, Palle E. T. 21 Kovařík, Hynek 21 Molchanov, Stanislav Alekseevich 21 Neidhardt, Hagen 21 Nenciu, Gheorghe 21 Pinchover, Yehuda 21 Zhao, Zhongxin 20 Behrndt, Jussi 20 Briet, Philippe 20 Cancès, Eric 20 Güneysu, Batu 20 Hainzl, Christian 20 Hoffmann-Ostenhof, Thomas 20 Lakaev, Saidakhmat Norzhigitovich 20 Lebowitz, Joel Louis 20 Remling, Christian 20 Sakhnovich, Alexander L. 20 Soffer, Avraham 19 Boutet de Monvel, Anne Marie 19 Cornean, Horia D. 19 Deift, Percy A. 19 Derevyagin, Maxim S. 19 Hempel, Rainer 19 Hoffmann-Ostenhof, Maria 19 Holden, Helge 19 Joye, Alain 19 Laptev, Ari 19 Liu, Wencai 19 Lotoreichik, Vladimir 19 Purice, Radu 19 Simanek, Brian Z. 19 Sjöstrand, Johannes ...and 8,429 more Authors
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#### Cited in 648 Serials

 985 Communications in Mathematical Physics 694 Journal of Mathematical Physics 683 Journal of Functional Analysis 371 Journal of Mathematical Analysis and Applications 301 Journal of Statistical Physics 233 Annales Henri Poincaré 232 Letters in Mathematical Physics 222 Journal of Differential Equations 203 Proceedings of the American Mathematical Society 189 Reviews in Mathematical Physics 181 Theoretical and Mathematical Physics 171 Communications in Partial Differential Equations 169 Transactions of the American Mathematical Society 164 Integral Equations and Operator Theory 157 Annales de l’Institut Henri Poincaré. Physique Théorique 115 Advances in Mathematics 114 Journal of Approximation Theory 110 Linear Algebra and its Applications 107 Journal of Mathematical Sciences (New York) 106 Duke Mathematical Journal 99 Mathematische Zeitschrift 94 Journal d’Analyse Mathématique 92 Archive for Rational Mechanics and Analysis 87 Mathematische Nachrichten 83 Journal of Spectral Theory 78 Mathematical Notes 75 Reports on Mathematical Physics 75 Mathematische Annalen 73 Functional Analysis and its Applications 71 Publications of the Research Institute for Mathematical Sciences, Kyoto University 70 Probability Theory and Related Fields 67 Potential Analysis 66 Mathematical Physics, Analysis and Geometry 63 The Annals of Probability 57 Complex Analysis and Operator Theory 56 Communications on Pure and Applied Mathematics 56 International Journal of Theoretical Physics 55 Journal de Mathématiques Pures et Appliquées. Neuvième Série 54 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 53 Annales de l’Institut Fourier 53 SIAM Journal on Mathematical Analysis 52 Annals of Physics 51 Journal of Computational and Applied Mathematics 50 Constructive Approximation 49 Ukrainian Mathematical Journal 49 Journal of Geometry and Physics 49 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 48 Calculus of Variations and Partial Differential Equations 47 Infinite Dimensional Analysis, Quantum Probability and Related Topics 45 Inventiones Mathematicae 45 Journal of Soviet Mathematics 45 Acta Applicandae Mathematicae 43 The Journal of Geometric Analysis 43 Stochastic Processes and their Applications 42 Applicable Analysis 42 Comptes Rendus. Mathématique. Académie des Sciences, Paris 40 Physics Letters. A 40 Bulletin of the American Mathematical Society. New Series 39 Mathematical Methods in the Applied Sciences 39 St. Petersburg Mathematical Journal 38 Journal of Pseudo-Differential Operators and Applications 36 Russian Journal of Mathematical Physics 35 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 35 Physica D 32 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 32 Doklady Mathematics 31 Israel Journal of Mathematics 31 Applied Mathematics and Computation 31 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 31 Discrete and Continuous Dynamical Systems 30 Ergodic Theory and Dynamical Systems 30 The Annals of Applied Probability 29 Positivity 29 Journal of the European Mathematical Society (JEMS) 28 Arkiv för Matematik 28 Journal of the American Mathematical Society 28 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 28 The Journal of Fourier Analysis and Applications 27 Manuscripta Mathematica 27 Monatshefte für Mathematik 27 Journal of Dynamics and Differential Equations 26 Memoirs of the American Mathematical Society 25 Rocky Mountain Journal of Mathematics 25 ZAMP. Zeitschrift für angewandte Mathematik und Physik 25 Journal of Theoretical Probability 25 Journal of Evolution Equations 25 Analysis and Mathematical Physics 24 Acta Mathematica 24 Annali di Matematica Pura ed Applicata. Serie Quarta 23 Transport Theory and Statistical Physics 23 Mathematics of Computation 23 Siberian Mathematical Journal 23 Geometric and Functional Analysis. GAFA 22 Nonlinearity 22 Nuclear Physics. B 22 Applied Mathematics Letters 22 Communications on Pure and Applied Analysis 22 Advances in Mathematical Physics 21 Results in Mathematics 20 Numerische Mathematik ...and 548 more Serials
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#### Cited in 62 Fields

 4,291 Partial differential equations (35-XX) 3,790 Quantum theory (81-XX) 3,759 Operator theory (47-XX) 1,510 Probability theory and stochastic processes (60-XX) 1,356 Statistical mechanics, structure of matter (82-XX) 1,123 Functional analysis (46-XX) 1,087 Ordinary differential equations (34-XX) 793 Global analysis, analysis on manifolds (58-XX) 594 Harmonic analysis on Euclidean spaces (42-XX) 559 Dynamical systems and ergodic theory (37-XX) 356 Linear and multilinear algebra; matrix theory (15-XX) 329 Numerical analysis (65-XX) 293 Special functions (33-XX) 275 Functions of a complex variable (30-XX) 271 Differential geometry (53-XX) 251 Fluid mechanics (76-XX) 226 Optics, electromagnetic theory (78-XX) 223 Difference and functional equations (39-XX) 195 Measure and integration (28-XX) 174 Potential theory (31-XX) 172 Relativity and gravitational theory (83-XX) 168 Calculus of variations and optimal control; optimization (49-XX) 165 Mechanics of particles and systems (70-XX) 153 Combinatorics (05-XX) 151 Topological groups, Lie groups (22-XX) 145 Approximations and expansions (41-XX) 120 Real functions (26-XX) 113 Integral equations (45-XX) 111 Number theory (11-XX) 105 Integral transforms, operational calculus (44-XX) 100 Abstract harmonic analysis (43-XX) 96 Statistics (62-XX) 95 Information and communication theory, circuits (94-XX) 93 Mechanics of deformable solids (74-XX) 78 Several complex variables and analytic spaces (32-XX) 78 Systems theory; control (93-XX) 70 Computer science (68-XX) 61 Biology and other natural sciences (92-XX) 57 Group theory and generalizations (20-XX) 55 Algebraic geometry (14-XX) 45 Manifolds and cell complexes (57-XX) 40 $$K$$-theory (19-XX) 37 Nonassociative rings and algebras (17-XX) 37 Convex and discrete geometry (52-XX) 37 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 33 Classical thermodynamics, heat transfer (80-XX) 32 Mathematical logic and foundations (03-XX) 32 Sequences, series, summability (40-XX) 31 Operations research, mathematical programming (90-XX) 30 Astronomy and astrophysics (85-XX) 22 Associative rings and algebras (16-XX) 19 Algebraic topology (55-XX) 17 General and overarching topics; collections (00-XX) 14 General topology (54-XX) 13 History and biography (01-XX) 13 Category theory; homological algebra (18-XX) 11 Geometry (51-XX) 9 Order, lattices, ordered algebraic structures (06-XX) 9 Geophysics (86-XX) 6 Field theory and polynomials (12-XX) 5 Commutative algebra (13-XX) 1 Mathematics education (97-XX)

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