Edit Profile (opens in new tab) Simon, Barry Co-Author Distance Author ID: simon.barry Published as: Simon, Barry; Simon, B. Homepage: http://math.caltech.edu/simon/simon.html External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 371 Publications since 1968, including 28 Books and 9 Additional arXiv Preprints 10 Contributions as Editor · 4 Further Contributions Biographic References: 8 Publications Co-Authors: 148 Co-Authors with 219 Joint Publications 3,965 Co-Co-Authors all top 5 Co-Authors 159 single-authored 34 Gesztesy, Fritz 16 Avron, Joseph E. 13 Zinchenko, Maxim 12 Christiansen, Jacob Stordal 12 Last, Yoram 10 Reed, Michael C. 9 Breuer, Jonathan 9 Davies, Edward Brian 9 Holden, Helge 8 Damanik, David 8 Kirsch, Werner 7 del Río Castillo, Rafael René 6 Hundertmark, Dirk 6 Jitomirskaya, Svetlana Yakovlevna 6 Killip, Rowan 5 Frank, Rupert L. 5 Guerra, Francesco 5 Laptev, Ari 5 Rosen, Lon M. 4 Deift, Percy A. 4 Herbst, Ira W. 4 Kiselev, Alexander A. 4 Kurasov, Pavel B. 4 Lieb, Elliott Hershel 4 Teschl, Gerald 4 Zhao, Zhongxin 3 Carmona, René A. 3 Craig, Walter 3 Enss, Volker 3 Harrell, Evans M. II 3 Hoffmann-Ostenhof, Maria 3 Hoffmann-Ostenhof, Thomas 3 Klaus, Martin 3 Molchanov, Stanislav Alekseevich 3 Naboko, Serguei N. 3 Perry, Peter A. 3 Pushnitski, Alexander B. 3 Sigal, Israel Michael 3 Souillard, Bernard 3 Stolz, Gunter 2 Alonso, Alberto 2 Avni, Nir 2 Barnsley, Michael Fielding 2 Bollé, D. 2 Böttcher, Albrecht 2 Delyon, François 2 Faris, William G. 2 Gordon, Alexander Ya. 2 Graf, Gian Michele 2 Grosse, Harald 2 Howland, James S. 2 Jaffe, Arthur Michael 2 Jakšić, Vojkan 2 Makarov, Nikolai Georgievich 2 Martínez-Finkelshtein, Andrei 2 Nachtergaele, Bruno 2 Nelson, Joseph Edward 2 Ramm, Alexander G. 2 Rosen, Jay S. 2 Ruelle, David Pierre 2 Sadun, L. 2 Schechter, Martin 2 Schweiger, Wolfgang 2 Seiler, Ruedi 2 Taylor, Michael Eugene 2 Vaĭnberg, Boris Rufimovich 2 Weder, Ricardo A. 2 Zeitouni, Ofer 2 Zlatoš, Andrej 1 Aizenman, A. 1 Aizenman, Michael 1 Avila, Artur 1 Banks, Jess 1 Basor, Estelle L. 1 Belibassakis, Konstadinos A. 1 Bellissard, Jean V. 1 Bentosela, François 1 Brown, Malcolm W. 1 Brownell, F. H. III 1 Brydges, David C. 1 Bulla, W. 1 Buss, Samuel R. 1 Cantero, María José 1 Carlen, Eric Anders 1 Connes, Alain 1 Cordes, Heinz Otto 1 Corngold, Noel 1 Corwin, Ivan Z. 1 Cranston, Michael Craig 1 Cycon, Hans L. 1 Davies, Ian M. 1 Denisov, Sergey A. 1 Devinatz, Allen 1 Diaconis, Persi Warren 1 Dolph, Charles L. 1 Duclos, Pierre 1 Ehrhardt, Torsten 1 Englisch, Harald 1 Evans, David E. 1 Friedland, Shmuel ...and 105 more Co-Authors all top 5 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 11 Annals of Mathematics. Second Series 9 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 Journal of Mathematical Physics 6 IMRN. International Mathematics Research Notices 5 Journal of Statistical Physics 5 Constructive Approximation 5 Journal of Physics A: Mathematical and General 5 Notices of the American Mathematical Society 5 Journal of Spectral Theory 4 Journal of Mathematical Analysis and Applications 4 Princeton Series in Physics 3 American Mathematical Monthly 3 Acta Mathematica 3 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 3 Inventiones Mathematicae 3 Journal of Computational and Applied Mathematics 3 Pacific Journal of Mathematics 3 Journal of Operator Theory 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Physical Review Letters 2 Wave Motion 2 Reviews in Mathematical Physics 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 2 Pure and Applied Functional Analysis 2 Operator Theory: Advances and Applications 1 Archive for Rational Mechanics and Analysis 1 Helvetica Physica Acta 1 Letters in Mathematical Physics 1 Russian Mathematical Surveys 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 The Ramanujan Journal 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 Notes (Princeton) 1 Mathematical Reports (Chur) 1 Mathematical Surveys and Monographs 1 Proceedings of Symposia in Pure Mathematics 1 Pure and Applied Mathematics (Academic Press) 1 Analysis & PDE 1 Springer Optimization and Its Applications all top 5 Fields 177 Operator theory (47-XX) 121 Partial differential equations (35-XX) 104 Quantum theory (81-XX) 69 Ordinary differential equations (34-XX) 48 Harmonic analysis on Euclidean spaces (42-XX) 42 Functional analysis (46-XX) 38 Probability theory and stochastic processes (60-XX) 28 Functions of a complex variable (30-XX) 24 Statistical mechanics, structure of matter (82-XX) 18 General and overarching topics; collections (00-XX) 18 Special functions (33-XX) 16 Difference and functional equations (39-XX) 15 History and biography (01-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 11 Real functions (26-XX) 11 Global analysis, analysis on manifolds (58-XX) 7 Combinatorics (05-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 Measure and integration (28-XX) 6 Approximations and expansions (41-XX) 5 Potential theory (31-XX) 4 Group theory and generalizations (20-XX) 4 Topological groups, Lie groups (22-XX) 4 General topology (54-XX) 4 Fluid mechanics (76-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 Integral transforms, operational calculus (44-XX) 2 Differential geometry (53-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 357 Publications have been cited 25,880 times in 15,974 Documents Cited by ▼ Year ▼ Methods of modern mathematical physics. IV: Analysis of operators. Zbl 0401.47001 Reed, Michael; Simon, Barry 3,028 1978 Methods of modern mathematical physics. II: Fourier analysis, self- adjointness. Zbl 0308.47002 Reed, Michael; Simon, Barry 2,513 1975 Methods of modern mathematical physics. I: Functional analysis. Rev. and enl. ed. Zbl 0459.46001 Reed, Michael; Simon, Barry 1,879 1980 Methods of modern mathematical physics. 1: Functional analysis. Zbl 0242.46001 Reed, Michael; Simon, Barry 1,545 1972 Methods of modern mathematical physics. III: Scattering theory. Zbl 0405.47007 Reed, Michael; Simon, Barry 887 1979 Schrödinger operators, with application to quantum mechanics and global geometry. Zbl 0619.47005 Cycon, H. L.; Froese, R. G.; Kirsch, W.; Simon, B. 747 1987 Schrödinger semigroups. Zbl 0524.35002 Simon, Barry 659 1982 Trace ideals and their applications. 2nd ed. Zbl 1074.47001 Simon, Barry 628 2005 Trace ideals and their applications. Zbl 0423.47001 Simon, Barry 547 1979 Orthogonal polynomials on the unit circle. Part 1: Classical theory. Zbl 1082.42020 Simon, Barry 528 2005 Functional integration and quantum physics. Zbl 0434.28013 Simon, Barry 484 1979 The \(P(\phi )_{2}\) Euclidean (quantum) field theory. Zbl 1175.81146 Simon, Barry 422 1974 Schrödinger operators with magnetic fields. I: General interactions. Zbl 0399.35029 Avron, J.; Herbst, I.; Simon, B. 260 1978 Orthogonal polynomials on the unit circle. Part 2: Spectral theory. Zbl 1082.42021 Simon, Barry 243 2005 Brownian motion and Harnack inequality for Schrödinger operators. Zbl 0459.60069 Aizenman, M.; Simon, B. 239 1982 The Thomas-Fermi theory of atoms, molecules and solids. Zbl 0938.81568 Lieb, Elliott H.; Simon, Barry 223 1977 Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians. Zbl 0568.47034 Davies, E. B.; Simon, B. 221 1984 The classical moment problem as a self-adjoint finite difference operator. Zbl 0910.44004 Simon, Barry 214 1998 Szegő’s theorem and its descendants. Spectral theory for \(L^2\) perturbations of orthogonal polynomials. Zbl 1230.33001 Simon, Barry 182 2011 The bound state of weakly coupled Schrödinger operators in one and two dimensions. Zbl 0325.35029 Simon, Barry 177 1976 Quantum mechanics for Hamiltonians defined as quadratic forms. Zbl 0232.47053 Simon, Barry 149 1971 The statistical mechanics of lattice gases. Vol. I. Zbl 0804.60093 Simon, Barry 149 1993 Inverse spectral analysis with partial information on the potential. II: The case of discrete spectrum. Zbl 0948.34060 Gesztesy, Fritz; Simon, Barry 149 2000 Spectral analysis of N-body Schrödinger operators. Zbl 0477.35069 Perry, P.; Sigal, I. M.; Simon, B. 139 1981 Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions. Zbl 0716.35006 Carmona, René; Masters, Wen Chen; Simon, Barry 138 1990 Almost periodic Schrödinger operators. II: The integrated density of states. Zbl 0544.35030 Avron, Joseph; Simon, Barry 138 1983 Sum rules for Jacobi matrices and their applications to spectral theory. Zbl 1050.47025 Killip, Rowan; Simon, Barry 137 2003 Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory. Zbl 0252.47009 Simon, Barry 136 1973 Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Zbl 0609.47001 Simon, Barry; Wolff, Tom 136 1986 A canonical decomposition for quadratic forms with applications to monotone convergence theorems. Zbl 0413.47029 Simon, Barry 132 1978 Semiclassical analysis of low lying eigenvalues. I: Non-degenerate minima: Asymptotic expansions. Zbl 0526.35027 Simon, Barry 131 1983 Notes on infinite determinants of Hilbert space operators. Zbl 0353.47008 Simon, Barry 128 1977 Representations of finite and compact groups. Zbl 0840.22001 Simon, Barry 123 1996 Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators. Zbl 0931.34066 Last, Yoram; Simon, Barry 118 1999 The analytic theory of matrix orthogonal polynomials. Zbl 1193.42097 Damanik, David; Pushnitski, Alexander; Simon, Barry 116 2008 The index of a pair of projections. Zbl 0822.47033 Avron, Joseph E.; Seiler, Ruedi; Simon, Barry 116 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 116 1996 Operator theory. A comprehensive course in analysis, part 4. Zbl 1334.00003 Simon, Barry 115 2015 Semiclassical analysis of low lying eigenvalues. II: Tunneling. Zbl 0626.35070 Simon, Barry 111 1984 Hypercontra ctive semigroups and two dimensional self-coupled Bose fields. Zbl 0241.47029 Simon, Barry; Høegh-Krohn, Raphael 108 1972 Spectral analysis of rank one perturbations and applications. Zbl 0824.47019 Simon, Barry 108 1995 Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case. Zbl 0455.35112 Klaus, M.; Simon, Barry 99 1980 Functional integration and quantum physics. 2nd ed. Zbl 1061.28010 Simon, Barry 97 2005 Almost periodic Schrödinger operators: A review. Zbl 0545.34023 Simon, Barry 95 1982 Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators. Zbl 0912.34074 Kiselev, Alexander; Last, Yoram; Simon, Barry 94 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. 92 1982 Weakly coupled bound states in quantum waveguides. Zbl 0868.35080 Bulla, W.; Gesztesy, F.; Renger, W.; Simon, B. 79 1997 Convexity. An analytic viewpoint. Zbl 1229.26003 Simon, Barry 78 2011 Kotani theory for one dimensional stochastic Jacobi matrices. Zbl 0534.60057 Simon, Barry 78 1983 CMV matrices: Five years after. Zbl 1125.15027 Simon, Barry 77 2007 Charge deficiency, charge transport and comparison of dimensions. Zbl 0822.47056 Avron, Joseph E.; Seiler, Ruedi; Simon, Barry 77 1994 The Birman-Krein-Vishik theory of self-adjoint extensions of semibounded operators. Zbl 0467.47017 Alonso, Alberto; Simon, Barry 76 1980 The classical limit of quantum partition functions. Zbl 0436.22012 Simon, Barry 75 1980 Scattering theory for systems with different spatial asymptotics on the left and right. Zbl 0393.34015 Davies, E. B.; Simon, B. 75 1978 Almost periodic Schrödinger operators. III: The absolutely continuous spectrum in one dimension. Zbl 0562.35026 Deift, P.; Simon, B. 74 1983 Cantor spectrum for the almost Mathieu equation. Zbl 0516.47018 Bellissard, J.; Simon, B. 72 1982 Maximal and minimal Schrödinger forms. Zbl 0446.35035 Simon, Barry 71 1979 A new approach to inverse spectral theory. I: Fundamental formalism. Zbl 0945.34013 Simon, Barry 68 1999 Large time behavior of the \(L^ p\) norm of Schrödinger semigroups. Zbl 0478.47024 Simon, Barry 68 1981 Phase space analysis of simple scattering systems: extensions of some work of Enss. Zbl 0402.35076 Simon, Barry 67 1979 Subharmonicity of the Lyapunov index. Zbl 0518.35027 Craig, W.; Simon, B. 67 1983 The Christoffel-Darboux kernel. Zbl 1159.42020 Simon, Barry 66 2008 Singular continuous spectrum for palindromic Schrödinger operators. Zbl 0839.11009 Hof, A.; Knill, Oliver; Simon, Barry 65 1995 On the measure of the spectrum for the almost Mathieu operator. Zbl 0724.47002 Avron, J.; von Mouche, P. H. M.; Simon, B. 64 1990 Operators with singular continuous spectrum. III: Almost periodic Schrödinger operators. Zbl 0830.34074 Jitomirskaya, Svetlana Ya.; Simon, Barry 64 1994 Operators with singular continuous spectrum. I: General operators. Zbl 0851.47003 Simon, Barry 63 1995 Some quantum operators with discrete spectrum but classically continuous spectrum. Zbl 0547.35039 Simon, Barry 63 1983 Almost periodic Schrödinger operators. I: Limit periodic potentials. Zbl 0484.35069 Avron, Joseph; Simon, Barry 62 1981 Comparison theorems for the gap of Schrödinger operators. Zbl 0661.35062 Kirsch, Werner; Simon, Barry 61 1987 Schrödinger operators with magnetic fields. III: Atoms in homogeneous magnetic field. Zbl 0464.35086 Avron, J. E.; Herbst, I. W.; Simon, B. 61 1981 Perturbations of orthogonal polynomials with periodic recursion coefficients. Zbl 1194.47031 Damanik, David; Killip, Rowan; Simon, Barry 60 2010 Basic complex analysis. A comprehensive course in analysis, part 2A. Zbl 1332.00004 Simon, Barry 58 2015 On positive eigenvalues of one body Schrödinger operators. Zbl 0167.11003 Simon, B. 58 1969 Resonances in one dimension and Fredholm determinants. Zbl 0977.34075 Simon, Barry 57 2000 \(m\)-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices. Zbl 0924.15005 Gesztesy, Fritz; Simon, Barry 57 1997 Equilibrium measures and capacities in spectral theory. Zbl 1149.31004 Simon, Barry 55 2007 Studies in mathematical physics. Essays in honor of Valentine Bargmann. Zbl 0326.00007 55 1976 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 54 2000 Distributions and their Hermite expansions. Zbl 0205.12901 Simon, B. 54 1971 Separation of center of mass in homogeneous magnetic fields. Zbl 0409.35027 Avron, J. E.; Herbst, I. W.; Simon, B. 53 1978 Schrödinger operators in the twentieth century. Zbl 0981.81025 Simon, Barry 51 2000 Brownian motion, \(L^p\) properties of Schrödinger operators and the localization of binding. Zbl 0446.47041 Simon, Barry 51 1980 The essential spectrum of Neumann Laplacians on some bounded singular domains. Zbl 0741.35043 Hempel, Rainer; Seco, Luis A.; Simon, Barry 50 1991 The essential spectrum of Schrödinger, Jacobi, and CMV operators. Zbl 1145.34052 Last, Yoram; Simon, Barry 50 2006 Schrödinger operators in the twenty-first century. Zbl 1074.81521 Simon, Barry 49 2000 Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061 Frank, Rupert L.; Simon, Barry 48 2017 Localization in general one-dimensional random systems. II: Continuum Schrödinger operators. Zbl 0637.60080 Kotani, S.; Simon, B. 47 1987 Nonclassical eigenvalue asymptotics. Zbl 0529.35064 Simon, Barry 47 1983 Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices. Zbl 0532.60057 Craig, Walter; Simon, Barry 47 1983 From power pure point to continuous spectrum in disordered systems. Zbl 0579.60056 Delyon, François; Simon, Barry; Souillard, Bernard 46 1985 Duality and singular continuous spectrum in the almost Mathieu equation. Zbl 0897.34074 Gordon, A. Y.; Jitomirskaya, S.; Last, Y.; Simon, B. 45 1997 Operators with singular continuous spectrum. II: Rank one operators. Zbl 1055.47500 del Río Castillo, Rafael René; Makarov, Nikolai G.; Simon, Barry 45 1994 Trace class perturbations and the absence of absolutely continuous spectra. Zbl 0684.47010 Simon, Barry; Spencer, Thomas 44 1989 Singular continuous spectrum for a class of almost periodic Jacobi matrices. Zbl 0491.47014 Avron, Joseph; Simon, Barry 44 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 44 1985 \(L^ p\) norms of non-critical Schrödinger semigroups. Zbl 0743.47047 Davies, E. B.; Simon, B. 43 1991 An abstract Kato’s inequality for generators of positivity preserving semigroups. Zbl 0389.47021 Simon, Barry 43 1977 The mathematical theory of resonances whose widths are exponentially small. Zbl 0455.35091 Harrell, E.; Simon, B. 43 1980 The \(\xi\) function. Zbl 0885.34070 Gesztesy, Fritz; Simon, Barry 43 1996 Essential self-adjointness of Schrödinger operators with positive potentials. Zbl 0234.47027 Simon, Barry 42 1973 Periodic boundary conditions for periodic Jacobi matrices on trees. Zbl 1507.47074 Avni, Nir; Breuer, Jonathan; Kalai, Gil; Simon, Barry 2 2022 Remembrances of Harold Widom. Zbl 1493.01041 Basor, Estelle; Böttcher, Albrecht; Corwin, Ivan; Diaconis, Persi; Ehrhardt, Torsten; Kelley, Al; Simon, Barry; Tracy, Craig A.; Tromba, Tony 2 2022 The strong Gauss-Lucas theorem and analyticity of correlation functions via the Lee-Yang theorem. Zbl 1507.82018 Simon, Barry 2 2022 Widom factors and Szegő-Widom asymptotics, a review. Zbl 07827907 Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim 1 2022 Twelve tales in mathematical physics: an expanded Heineman Prize lecture. Zbl 1507.01028 Simon, Barry 1 2022 Remarks on periodic Jacobi matrices on trees. Zbl 1462.81095 Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim 3 2021 Periodic Jacobi matrices on trees. Zbl 1512.47056 Avni, Nir; Breuer, Jonathan; Simon, Barry 11 2020 Asymptotics of Chebyshev polynomials. III: Sets saturating Szegő, Schiefermayr, and Totik-Widom bounds. Zbl 1448.41026 Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim 10 2020 Asymptotics of Chebyshev polynomials. IV: Comments on the complex case. Zbl 1472.30001 Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim 9 2020 Proof of the strong Scott conjecture for Chandrasekhar atoms. Zbl 1465.81076 Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz; Simon, Barry 7 2020 Loewner’s theorem on monotone matrix functions. Zbl 1428.26002 Simon, Barry 31 2019 Asymptotics of Chebyshev polynomials. II: DCT subsets of \(\mathbb{R}\). Zbl 1426.41035 Christiansen, Jacob S.; Simon, Barry; Yuditskii, Peter; Zinchenko, Maxim 14 2019 Poncelet’s theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators. Zbl 1497.47012 Martínez-Finkelshtein, Andrei; Simanek, Brian; Simon, Barry 12 2019 Analysis and operator theory. Dedicated in memory of Tosio Kato’s 100th birthday. With a foreword by Barry Simon. Zbl 1419.47002 6 2019 Tosio Kato’s work on non-relativistic quantum mechanics. II. Zbl 1472.81094 Simon, Barry 5 2019 Alexander Gordon. Zbl 1451.01022 Jitomirskaya, Svetlana; Molchanov, Stanislav A.; Simon, Barry; Vainberg, Boris R. 1 2019 Tosio Kato’s work on non-relativistic quantum mechanics. I. Zbl 1416.81063 Simon, Barry 13 2018 Large deviations and the Lukic conjecture. Zbl 1426.60032 Breuer, Jonathan; Simon, Barry; Zeitouni, Ofer 10 2018 Large deviations and sum rules for spectral theory: a pedagogical approach. Zbl 1402.60029 Breuer, Jonathan; Simon, Barry; Zeitouni, Ofer 9 2018 Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061 Frank, Rupert L.; Simon, Barry 48 2017 Asymptotics of Chebyshev polynomials. I: Subsets of \({\mathbb {R}}\). Zbl 1369.41031 Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim 28 2017 Unitaries permuting two orthogonal projections. Zbl 06950136 Simon, Barry 13 2017 Similarity between two projections. Zbl 1508.47021 Böttcher, Albrecht; Simon, Barry; Spitkovsky, Ilya 11 2017 A coupled-mode model for water wave scattering by vertically sheared currents in variable bathymetry regions. Zbl 1524.76061 Belibassakis, K. A.; Simon, B.; Touboul, J.; Rey, V. 5 2017 Condensation of fermion pairs in a domain. Zbl 1372.82044 Frank, Rupert L.; Lemm, Marius; Simon, Barry 4 2017 A Cayley-Hamiltonian theorem for periodic finite band matrices. Zbl 1376.15008 Simon, Barry 1 2017 Operator theory. A comprehensive course in analysis, part 4. Zbl 1334.00003 Simon, Barry 115 2015 Basic complex analysis. A comprehensive course in analysis, part 2A. Zbl 1332.00004 Simon, Barry 58 2015 Harmonic analysis. A comprehensive course in analysis, part 3. Zbl 1334.00002 Simon, Barry 37 2015 Real analysis. A comprehensive course in analysis, part 1. Zbl 1332.00003 Simon, Barry 36 2015 Advanced complex analysis. A comprehensive course in analysis, part 2B. Zbl 1332.00005 Simon, Barry 16 2015 Cantor polynomials and some related classes of OPRL. Zbl 1309.42034 Krüger, Helge; Simon, Barry 10 2015 The ultimate companion to “A comprehensive course in analysis. A five-volume reference set”. Zbl 1331.00001 Simon, Barry 2 2015 Stability of asymptotics of Christoffel-Darboux kernels. Zbl 1412.60053 Breuer, Jonathan; Last, Yoram; Simon, Barry 6 2014 Spectral theory of orthogonal polynomials. Zbl 1301.31003 Simon, B. 3 2014 Spectral analysis, differential equations and mathematical physics: A Festschrift in honor of Fritz Gesztesy’s 60th birthday. Zbl 1270.00040 6 2013 Finite gap Jacobi matrices: a review. Zbl 1319.47028 Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim 6 2013 Finite gap Jacobi matrices. III: Beyond the Szegő class. Zbl 1238.42009 Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim 9 2012 Szegő’s theorem and its descendants. Spectral theory for \(L^2\) perturbations of orthogonal polynomials. Zbl 1230.33001 Simon, Barry 182 2011 Convexity. An analytic viewpoint. Zbl 1229.26003 Simon, Barry 78 2011 Finite gap Jacobi matrices. II: The Szegő class. Zbl 1236.42021 Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim 18 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 12 2011 Natural boundaries and spectral theory. Zbl 1219.30001 Breuer, Jonathan; Simon, Barry 11 2011 Asymptotics of the \(L^2\) norm of derivatives of OPUC. Zbl 1220.42019 Martínez-Finkelshtein, Andrei; Simon, Barry 4 2011 On the removal of finite discrete spectrum by coefficient stripping. Zbl 1277.47046 Simon, Barry 1 2011 Perturbations of orthogonal polynomials with periodic recursion coefficients. Zbl 1194.47031 Damanik, David; Killip, Rowan; Simon, Barry 60 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 29 2010 Finite gap Jacobi matrices. I: The isospectral torus. Zbl 1200.42012 Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim 27 2010 Equality of the spectral and dynamical definitions of reflection. Zbl 1190.47032 Breuer, Jonathan; Ryckman, Eric; Simon, Barry 20 2010 The Nevai condition. Zbl 1198.42021 Breuer, Jonathan; Last, Yoram; Simon, Barry 16 2010 The Hilbert transform of a measure. Zbl 1211.30052 Poltoratski, Alexei; Simon, Barry; Zinchenko, Maxim 13 2010 Fine structure of the zeros of orthogonal polynomials: a progress report. Zbl 1204.42042 Simon, Barry 2 2010 Sum rules and spectral measures of Schrödinger operators with \(L^2\) potentials. Zbl 1185.34131 Killip, Rowan; Simon, Barry 25 2009 Weak convergence of CD kernels and applications. Zbl 1158.33003 Simon, Barry 25 2009 Schrödinger operators with purely discrete spectrum. Zbl 1199.47198 Simon, Barry 14 2009 Regularity and the Cesàro-Nevai class. Zbl 1167.42010 Simon, Barry 7 2009 Finite gap Jacobi matrices: An announcement. Zbl 1174.42028 Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim 5 2009 Monotone Jacobi parameters and non-Szegő weights. Zbl 1185.42027 Kreimer, Yury; Last, Yoram; Simon, Barry 3 2009 Poisson brackets of orthogonal polynomials. Zbl 1200.41040 Cantero, María José; Simon, Barry 2 2009 A celebration of Jürg and Tom. Zbl 1166.82300 Simon, Barry 1 2009 The analytic theory of matrix orthogonal polynomials. Zbl 1193.42097 Damanik, David; Pushnitski, Alexander; Simon, Barry 116 2008 The Christoffel-Darboux kernel. Zbl 1159.42020 Simon, Barry 66 2008 Two extensions of Lubinsky’s universality theorem. Zbl 1168.42304 Simon, Barry 41 2008 Fine structure of the zeros of orthogonal polynomials. IV: A priori bounds and clock behavior. Zbl 1214.42044 Last, Yoram; Simon, Barry 26 2008 On the Koplienko spectral shift function. I: Basics. Zbl 1190.47016 Gesztesy, F.; Pushnitski, A.; Simon, B. 21 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 20 2008 Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices. Zbl 1135.47026 Hundertmark, Dirk; Simon, Barry 13 2008 CMV matrices: Five years after. Zbl 1125.15027 Simon, Barry 77 2007 Equilibrium measures and capacities in spectral theory. Zbl 1149.31004 Simon, Barry 55 2007 Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle. Zbl 1110.33004 Simon, Barry 29 2007 Orthogonal polynomials with exponentially decaying recursion coefficients. Zbl 1143.42306 Simon, Barry 13 2007 Zeros of OPUC and long time asymptotics of Schur and related flows. Zbl 1125.35098 Simon, Barry 7 2007 Meromorphic Jost functions and asymptotic expansions for Jacobi parameters. Zbl 1255.47031 Simon, Barry 2 2007 Fine structure of the zeros of orthogonal polynomials: a review. Zbl 1214.42052 Simon, Barry 1 2007 The essential spectrum of Schrödinger, Jacobi, and CMV operators. Zbl 1145.34052 Last, Yoram; Simon, Barry 50 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 27 2006 Fine structure of the zeros of orthogonal polynomials. I: A tale of two pictures. Zbl 1129.42011 Simon, Barry 22 2006 Jost functions and Jost solutions for Jacobi matrices. II: Decay and analyticity. Zbl 1122.47030 Damanik, David; Simon, Barry 22 2006 Diffusion, quantum theory, and radically elementary mathematics. Zbl 1104.81003 22 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. 18 2006 Aizenman’s theorem for orthogonal polynomials on the unit circle. Zbl 1104.42014 Simon, Barry 16 2006 Fine structure of the zeros of orthogonal polynomials. III: Periodic recursion coefficients. Zbl 1129.42013 Simon, Barry 11 2006 Trace ideals and their applications. 2nd ed. Zbl 1074.47001 Simon, Barry 628 2005 Orthogonal polynomials on the unit circle. Part 1: Classical theory. Zbl 1082.42020 Simon, Barry 528 2005 Orthogonal polynomials on the unit circle. Part 2: Spectral theory. Zbl 1082.42021 Simon, Barry 243 2005 Functional integration and quantum physics. 2nd ed. Zbl 1061.28010 Simon, Barry 97 2005 OPUC on one foot. Zbl 1108.42005 Simon, Barry 41 2005 Sturm oscillation and comparison theorems. Zbl 1117.39013 Simon, Barry 17 2005 On a theorem of Kac and Gilbert. Zbl 1071.47027 Simon, Barry 14 2005 Schrödinger operators with few bound states. Zbl 1082.47029 Damanik, David; Killip, Rowan; Simon, Barry 12 2005 Higher-order Szegő theorems with two singular points. Zbl 1067.30075 Simon, Barry; Zlatoš, Andrej 12 2005 Fine structure of the zeros of orthogonal polynomials. II: OPUC with competing exponential decay. Zbl 1129.42012 Simon, Barry 7 2005 Meromorphic Szegő functions and asymptotic series for Verblunsky coefficients. Zbl 1117.42005 Simon, Barry 4 2005 Limits of zeros of orthogonal polynomials on the circle. Zbl 1077.42017 Simon, Barry; Totik, Vilmos 2 2005 The sharp form of the strong Szegő theorem. Zbl 1093.47032 Simon, Barry 2 2005 A diamagnetic inequality for semigroup differences. Zbl 1068.47052 Hundertmark, Dirk; Simon, Barry 26 2004 Orthogonal polynomials on the unit circle: new results. Zbl 1086.42501 Simon, Barry 21 2004 Analogs of the \(m\)-function in the theory of orthogonal polynomials on the unit circle. Zbl 1055.33010 Simon, Barry 18 2004 A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices. Zbl 1064.30030 Simon, Barry 14 2004 Ratio asymptotics and weak asymptotic measures for orthogonal polynomials on the real line. Zbl 1043.42017 Simon, Barry 13 2004 ...and 257 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 11,915 Authors 200 Simon, Barry 125 Albeverio, Sergio A. 120 Gesztesy, Fritz 90 Damanik, David 77 Exner, Pavel 75 Sukochev, Fedor Anatol’evich 65 Frank, Rupert L. 61 Helffer, Bernard 60 Fröhlich, Jürg Martin 58 Korotyaev, Evgeny L. 54 Davies, Edward Brian 54 Sigal, Israel Michael 50 Lewin, Mathieu 49 Jitomirskaya, Svetlana Yakovlevna 46 Arai, Asao 46 Lieb, Elliott Hershel 46 Yang, Chuanfu 44 Klein, Abel 39 Borisov, Denis Ivanovich 39 Herbst, Ira W. 39 Nazarov, Sergeĭ Aleksandrovich 38 de Oliveira, César R. 38 Marcellán Español, Francisco 38 Yafaev, Dimitri R. 37 Gérard, Christian 36 Lubinsky, Doron S. 36 Solovej, Jan Philip 36 Stolz, Gunter 35 Lenz, Daniel H. 35 Seiringer, Robert 35 Wei, Guangsheng 35 Zanin, Dmitriy V. 34 Behrndt, Jussi 34 Ding, Yanheng 34 Kirsch, Werner 34 Toft, Joachim 34 Weder, Ricardo A. 34 Weinstein, Michael I. 33 Krejčiřík, David 33 Raikov, Georgi D. 32 Fournais, Søren 32 Lakaev, Saidakhmat Norzhigitovich 32 Sobolev, Alexander V. 31 Denisov, Sergey A. 31 Hiroshima, Fumio 31 Röckner, Michael 31 Song, Renming 30 Chen, Zhen-Qing 30 Fillman, Jake 30 Jakšić, Vojkan 30 Kittaneh, Fuad 30 Last, Yoram 30 Siedentop, Heinz Karl Heinrich 30 Teschl, Gerald 30 Zinchenko, Maxim 29 Carey, Alan L. 29 Klopp, Frédéric 29 Laptev, Ari 29 Schulz-Baldes, Hermann 29 Sri Ranga, Alagacone 28 Cancès, Eric 28 Kondrat’yev, Yuriĭ Grygorovych 28 Kovařík, Hynek 28 Lotoreichik, Vladimir 28 Naboko, Serguei N. 28 Nakamura, Shu 28 Pushnitski, Alexander B. 28 Veselić, Ivan 26 Cornean, Horia D. 26 Faupin, Jérémy 26 Harrell, Evans M. II 26 Hislop, Peter D. 26 Liu, Wencai 26 Vugal’ter, Semën Abramovich 25 Hundertmark, Dirk 25 Jensen, Arne 25 Malamud, Mark M. 25 Molchanov, Stanislav Alekseevich 25 Neidhardt, Hagen 25 Skibsted, Erik 24 Breuer, Jonathan 24 Briet, Philippe 24 Gadella, Manuel 24 Güneysu, Batu 24 Jørgensen, Palle E. T. 24 Michelangeli, Alessandro 24 Miyao, Tadahiro 24 Pillet, Claude-Alain 24 Pinchover, Yehuda 24 Spohn, Herbert 24 Stochel, Jan 24 Stollmann, Peter 24 Tamura, Hideo 23 Bach, Volker 23 Bagarello, Fabio 23 Demuth, Michael 23 Hainzl, Christian 23 Hasler, David G. 23 Ichinose, Takashi 23 Lebowitz, Joel Louis ...and 11,815 more Authors all top 5 Cited in 782 Serials 1,093 Communications in Mathematical Physics 927 Journal of Functional Analysis 905 Journal of Mathematical Physics 538 Journal of Mathematical Analysis and Applications 337 Journal of Differential Equations 325 Journal of Statistical Physics 320 Annales Henri Poincaré 276 Letters in Mathematical Physics 228 Reviews in Mathematical Physics 225 Proceedings of the American Mathematical Society 191 Theoretical and Mathematical Physics 191 Transactions of the American Mathematical Society 184 Advances in Mathematics 182 Integral Equations and Operator Theory 182 Communications in Partial Differential Equations 171 Linear Algebra and its Applications 170 Reports on Mathematical Physics 157 Annales de l’Institut Henri Poincaré. 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Neuvième Série 80 SIAM Journal on Mathematical Analysis 78 Communications on Pure and Applied Mathematics 78 Probability Theory and Related Fields 77 Journal of Computational and Applied Mathematics 76 Mathematical Physics, Analysis and Geometry 75 The Annals of Probability 74 Journal of Geometry and Physics 74 Publications of the Research Institute for Mathematical Sciences, Kyoto University 72 Physica D 67 Calculus of Variations and Partial Differential Equations 62 Annales de l’Institut Fourier 62 Constructive Approximation 62 The Journal of Geometric Analysis 61 International Journal of Theoretical Physics 61 Inventiones Mathematicae 60 Nonlinearity 59 Applicable Analysis 59 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 59 Infinite Dimensional Analysis, Quantum Probability and Related Topics 56 Ukrainian Mathematical Journal 55 Comptes Rendus. Mathématique. Académie des Sciences, Paris 54 Nuclear Physics. B 51 St. Petersburg Mathematical Journal 51 Journal of Pseudo-Differential Operators and Applications 48 Acta Applicandae Mathematicae 48 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 46 Russian Journal of Mathematical Physics 45 Journal of Soviet Mathematics 45 Journal of High Energy Physics 45 Analysis and Mathematical Physics 43 Journal of Computational Physics 43 Discrete and Continuous Dynamical Systems 42 The Journal of Fourier Analysis and Applications 42 Journal of the European Mathematical Society (JEMS) 41 Journal of Evolution Equations 40 Applied Mathematics and Computation 40 Bulletin of the American Mathematical Society. New Series 39 Positivity 38 Operators and Matrices 37 Israel Journal of Mathematics 37 The Annals of Applied Probability 36 Doklady Mathematics 36 Communications on Pure and Applied Analysis 36 Nonlinear Analysis. Theory, Methods & Applications 35 Linear and Multilinear Algebra 35 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 35 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 35 Journal of Dynamics and Differential Equations 34 ZAMP. Zeitschrift für angewandte Mathematik und Physik 34 Lobachevskii Journal of Mathematics 33 Annali di Matematica Pura ed Applicata. Serie Quarta 33 Results in Mathematics 33 Ergodic Theory and Dynamical Systems 32 Classical and Quantum Gravity 32 Memoirs of the American Mathematical Society 32 Electronic Journal of Probability 32 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 31 Arkiv för Matematik 31 Monatshefte für Mathematik 31 Applied Mathematics Letters 31 International Journal of Geometric Methods in Modern Physics 30 Journal of Theoretical Probability ...and 682 more Serials all top 5 Cited in 63 Fields 5,916 Partial differential equations (35-XX) 5,208 Quantum theory (81-XX) 5,000 Operator theory (47-XX) 2,047 Probability theory and stochastic processes (60-XX) 1,799 Statistical mechanics, structure of matter (82-XX) 1,602 Functional analysis (46-XX) 1,412 Ordinary differential equations (34-XX) 1,043 Global analysis, analysis on manifolds (58-XX) 855 Dynamical systems and ergodic theory (37-XX) 836 Harmonic analysis on Euclidean spaces (42-XX) 529 Linear and multilinear algebra; matrix theory (15-XX) 507 Numerical analysis (65-XX) 438 Special functions (33-XX) 416 Functions of a complex variable (30-XX) 399 Differential geometry (53-XX) 342 Fluid mechanics (76-XX) 340 Optics, electromagnetic theory (78-XX) 301 Difference and functional equations (39-XX) 284 Relativity and gravitational theory (83-XX) 273 Measure and integration (28-XX) 265 Mechanics of particles and systems (70-XX) 255 Calculus of variations and optimal control; optimization (49-XX) 246 Potential theory (31-XX) 245 Combinatorics (05-XX) 225 Topological groups, Lie groups (22-XX) 216 Real functions (26-XX) 208 Approximations and expansions (41-XX) 178 Statistics (62-XX) 165 Abstract harmonic analysis (43-XX) 159 Integral equations (45-XX) 156 Number theory (11-XX) 156 Integral transforms, operational calculus (44-XX) 149 Mechanics of deformable solids (74-XX) 140 Information and communication theory, circuits (94-XX) 137 Systems theory; control (93-XX) 131 Several complex variables and analytic spaces (32-XX) 112 Computer science (68-XX) 107 Algebraic geometry (14-XX) 105 Biology and other natural sciences (92-XX) 100 Group theory and generalizations (20-XX) 72 Manifolds and cell complexes (57-XX) 67 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 63 Nonassociative rings and algebras (17-XX) 63 Convex and discrete geometry (52-XX) 56 Operations research, mathematical programming (90-XX) 52 \(K\)-theory (19-XX) 49 Classical thermodynamics, heat transfer (80-XX) 44 Mathematical logic and foundations (03-XX) 43 Associative rings and algebras (16-XX) 42 Sequences, series, summability (40-XX) 42 Astronomy and astrophysics (85-XX) 41 General and overarching topics; collections (00-XX) 31 Algebraic topology (55-XX) 30 History and biography (01-XX) 24 Geometry (51-XX) 24 General topology (54-XX) 22 Category theory; homological algebra (18-XX) 20 Geophysics (86-XX) 14 Order, lattices, ordered algebraic structures (06-XX) 12 Commutative algebra (13-XX) 9 Field theory and polynomials (12-XX) 3 Mathematics education (97-XX) 1 General algebraic systems (08-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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