The Spectral Theory Of Toeplitz Operators Am 99 Volume 99

Author : L. Boutet de Monvel,Victor Guillemin
Publisher : Princeton University Press
Page : 166 pages
File Size : 53,8 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881444

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The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 by L. Boutet de Monvel,Victor Guillemin Pdf

The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations. If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol. It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.

Author : L. Boutet de Monvel,Victor Guillemin
Publisher : Unknown
Page : 160 pages
File Size : 44,9 Mb
Release : 1981
Category : Mathematics
ISBN : 0691082847

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The Spectral Theory of Toeplitz Operators by L. Boutet de Monvel,Victor Guillemin Pdf

The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations. If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol. It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.

Author : Yohann Le Floch
Publisher : Springer
Page : 142 pages
File Size : 44,7 Mb
Release : 2018-09-19
Category : Mathematics
ISBN : 9783319946825

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A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds by Yohann Le Floch Pdf

This text provides a comprehensive introduction to Berezin–Toeplitz operators on compact Kähler manifolds. The heart of the book is devoted to a proof of the main properties of these operators which have been playing a significant role in various areas of mathematics such as complex geometry, topological quantum field theory, integrable systems, and the study of links between symplectic topology and quantum mechanics. The book is carefully designed to supply graduate students with a unique accessibility to the subject. The first part contains a review of relevant material from complex geometry. Examples are presented with explicit detail and computation; prerequisites have been kept to a minimum. Readers are encouraged to enhance their understanding of the material by working through the many straightforward exercises.

Author : Uwe Kähler,Michael Reissig,Irene Sabadini,Jasson Vindas
Publisher : Springer Nature
Page : 696 pages
File Size : 40,8 Mb
Release : 2023-12-01
Category : Mathematics
ISBN : 9783031363757

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Analysis, Applications, and Computations by Uwe Kähler,Michael Reissig,Irene Sabadini,Jasson Vindas Pdf

This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

Author : Kengo Hirachi
Publisher : Springer Nature
Page : 372 pages
File Size : 54,7 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9789819995066

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The Bergman Kernel and Related Topics by Kengo Hirachi Pdf

Author : Michael Hitrik,Dmitry Tamarkin,Boris Tsygan,Steve Zelditch
Publisher : Springer
Page : 654 pages
File Size : 40,6 Mb
Release : 2018-12-19
Category : Mathematics
ISBN : 9783030015886

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Algebraic and Analytic Microlocal Analysis by Michael Hitrik,Dmitry Tamarkin,Boris Tsygan,Steve Zelditch Pdf

This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University. Featured papers expand on mini-courses and talks ranging from foundational material to advanced research-level papers, and new applications in symplectic geometry, mathematical physics, partial differential equations, and complex analysis are discussed in detail. Topics include Procesi bundles and symplectic reflection algebras, microlocal condition for non-displaceability, polarized complex manifolds, nodal sets of Laplace eigenfunctions, geodesics in the space of Kӓhler metrics, and partial Bergman kernels. This volume is a valuable resource for graduate students and researchers in mathematics interested in understanding microlocal analysis and learning about recent research in the area.

Author : Mikhail Vladimirovich Karasev,V. P. Maslov
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 51,8 Mb
Release : 1993
Category : Mathematics
ISBN : 0821845969

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Nonlinear Poisson Brackets by Mikhail Vladimirovich Karasev,V. P. Maslov Pdf

This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.

Author : Nalini Anantharaman,Ashkan Nikeghbali,Michael Th. Rassias
Publisher : Springer Nature
Page : 449 pages
File Size : 43,8 Mb
Release : 2020-11-21
Category : Mathematics
ISBN : 9783030564094

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Frontiers in Analysis and Probability by Nalini Anantharaman,Ashkan Nikeghbali,Michael Th. Rassias Pdf

The volume presents extensive research devoted to a broad spectrum of mathematical analysis and probability theory. Subjects discussed in this Work are those treated in the so-called Strasbourg–Zürich Meetings. These meetings occur twice yearly in each of the cities, Strasbourg and Zürich, venues of vibrant mathematical communication and worldwide gatherings. The topical scope of the book includes the study of monochromatic random waves defined for general Riemannian manifolds, notions of entropy related to a compact manifold of negative curvature, interacting electrons in a random background, lp-cohomology (in degree one) of a graph and its connections with other topics, limit operators for circular ensembles, polyharmonic functions for finite graphs and Markov chains, the ETH-Approach to Quantum Mechanics, 2-dimensional quantum Yang–Mills theory, Gibbs measures of nonlinear Schrödinger equations, interfaces in spectral asymptotics and nodal sets. Contributions in this Work are composed by experts from the international community, who have presented the state-of-the-art research in the corresponding problems treated. This volume is expected to be a valuable resource to both graduate students and research mathematicians working in analysis, probability as well as their interconnections and applications.

Author : Mihail Vladimirovi_ Karasev,Viktor Pavlovi_ Maslov,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 382 pages
File Size : 45,9 Mb
Release : 2012-06-06
Category : Education
ISBN : 9780821887967

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Nonlinear Poisson Brackets by Mihail Vladimirovi_ Karasev,Viktor Pavlovi_ Maslov,American Mathematical Society Pdf

This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.

Author : Pietro Aiena
Publisher : Springer
Page : 546 pages
File Size : 40,8 Mb
Release : 2018-11-24
Category : Mathematics
ISBN : 9783030022662

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Fredholm and Local Spectral Theory II by Pietro Aiena Pdf

This monograph concerns the relationship between the local spectral theory and Fredholm theory of bounded linear operators acting on Banach spaces. The purpose of this book is to provide a first general treatment of the theory of operators for which Weyl-type or Browder-type theorems hold. The product of intensive research carried out over the last ten years, this book explores for the first time in a monograph form, results that were only previously available in journal papers. Written in a simple style, with sections and chapters following an easy, natural flow, it will be an invaluable resource for researchers in Operator Theory and Functional Analysis. The reader is assumed to be familiar with the basic notions of linear algebra, functional analysis and complex analysis.

Author : Jeffrey Rauch,Barry Simon
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461219408

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Quasiclassical Methods by Jeffrey Rauch,Barry Simon Pdf

This IMA Volume in Mathematics and its Applications QUASICLASSICAL METHODS is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Jeffrey Rauch and Barry Simon for their excellent work as organizers of the meeting. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE There are a large number of problems where qualitative features of a partial differential equation in an appropriate regime are determined by the behavior of an associated ordinary differential equation. The example which gives the area its name is the limit of quantum mechanical Hamil tonians (Schrodinger operators) as Planck's constant h goes to zero, which is determined by the corresponding classical mechanical system. A sec ond example is linear wave equations with highly oscillatory initial data. The solutions are described by geometric optics whose centerpiece are rays which are solutions of ordinary differential equations analogous to the clas sical mechanics equations in the example above. Much recent work has concerned with understanding terms beyond the leading term determined by the quasi classical limit. Two examples of this involve Weyl asymptotics and the large-Z limit of atomic Hamiltonians, both areas of current research.

Author : Kunyu Guo,Hansong Huang
Publisher : Springer
Page : 322 pages
File Size : 51,5 Mb
Release : 2015-06-23
Category : Mathematics
ISBN : 9783662468456

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Multiplication Operators on the Bergman Space by Kunyu Guo,Hansong Huang Pdf

This book deals with various aspects of commutants and reducing subspaces of multiplication operators on the Bergman space, along with relevant von Neumann algebras generated by these operators, which have been the focus of considerable attention from the authors and other experts in recent years. The book reviews past developments and offers insights into cutting-edge developments in the study of multiplication operators. It also provides commentary and comparisons to stimulate research in this area.

Author : Estelle Basor,Albrecht Böttcher,Torsten Ehrhardt,Craig A. Tracy
Publisher : Springer Nature
Page : 606 pages
File Size : 48,5 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 9783031138515

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Toeplitz Operators and Random Matrices by Estelle Basor,Albrecht Böttcher,Torsten Ehrhardt,Craig A. Tracy Pdf

This volume is dedicated to the memory of Harold Widom (1932–2021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time. It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg–Ising chain. Widom's most famous contributions were made to Toeplitz operators and random matrices. While his work on random matrices is part of almost all the present-day research activities in this field, his work in Toeplitz operators and matrices was done mainly before 2000 and is therefore described in a contribution devoted to his achievements in just this area. The volume contains 18 invited and refereed research and expository papers on Toeplitz operators and random matrices. These present new results or new perspectives on topics related to Widom's work.

Author : Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar
Publisher : Springer Nature
Page : 893 pages
File Size : 55,6 Mb
Release : 2024-01-22
Category : Mathematics
ISBN : 9783031505355

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Multivariable Operator Theory by Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar Pdf

Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Author : Zeev Ditzian
Publisher : American Mathematical Soc.
Page : 416 pages
File Size : 47,6 Mb
Release : 1983
Category : Mathematics
ISBN : 0821860046

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Second Edmonton Conference on Approximation Theory by Zeev Ditzian Pdf

The Second Edmonton Conference on Approximation Theory, held in Edmonton, Alberta, June 7-11, 1982, was devoted to Approximation Theory and related topics, including spline approximation, computational problems, complex and rational approximation, and techniques from harmonic analysis and the theory of interpolation of operators. In conformity with the requirements of this series, this volume consists of refereed papers by a selection of the invited speakers. The conference was sponsored by the Canadian Mathematical Society and supported by grants from the Natural Sciences and Engineering Research Council of Canada and the University of Alberta.