The Spectral Theory Of Toeplitz Operators
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The Spectral Theory Of Toeplitz Operators Am 99 Volume 99
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Author : L. Boutet de Monvel
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
The Spectral Theory Of Toeplitz Operators Am 99 Volume 99 written by L. Boutet de Monvel and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
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.
Carleson Curves Muckenhoupt Weights And Toeplitz Operators
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Author : Albrecht Böttcher
language : en
Publisher: Birkhäuser
Release Date : 1997-09-01
Carleson Curves Muckenhoupt Weights And Toeplitz Operators written by Albrecht Böttcher and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-01 with Mathematics categories.
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 1997. This book is a self-contained exposition of the spectral theory of Toeplitz operators with piecewise continuous symbols and singular integral operators with piecewise continuous coefficients. It includes an introduction to Carleson curves, Muckenhoupt weights, weighted norm inequalities, local principles, Wiener-Hopf factorization, and Banach algebras generated by idempotents. Some basic phenomena in the field and the techniques for treating them came to be understood only in recent years and are comprehensively presented here for the first time. The material has been polished in an effort to make advanced topics accessible to a broad readership. The book is addressed to a wide audience of students and mathematicians interested in real and complex analysis, functional analysis and operator theory.
A Spectral Theory For Toeplitz Operators
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Author : Edward Kevan Billowitz
language : en
Publisher:
Release Date : 1967
A Spectral Theory For Toeplitz Operators written by Edward Kevan Billowitz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Transformations (Mathematics) categories.
A Short Course On Spectral Theory
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Author : William Arveson
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-09
A Short Course On Spectral Theory written by William Arveson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-09 with Mathematics categories.
This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here.
The Spectral Theory Of Toeplitz Operators
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Author : Anthony Bak
language : en
Publisher:
Release Date : 1981
The Spectral Theory Of Toeplitz Operators written by Anthony Bak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Forms (Mathematics) categories.
Toeplitz Operators And Spectral Function Theory
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Author : N. Nikolsky
language : en
Publisher: Birkhäuser
Release Date : 2013-12-01
Toeplitz Operators And Spectral Function Theory written by N. Nikolsky and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Social Science categories.
The volume contains selected papers of the Spectral Function Theory seminar, Leningrad Branch of Steklov Mathematical Institute. The papers are mostly devoted to the theory of Toeplitz and model operators. These subjects are considered here from various points of view. Several papers concern the relationships of Toeplitz operators to weighted polynomial approximation. Namely, two papers by B. Solomyak and A. Volberg intensively treat the problem of spectra! multiplicity f~r analytic Toeplitz operators (which are, in fact, multiplication operators) and my paper can serve as an introduction to the problem. This theme of multiplicities is continued in a paper by V. Vasyunin where the multiplicity of the spectrum is computed for Hilbert space contractions with finite defect indices. V. Peller's paper deals with a perturbation theory problem for Toeplitz operators. In a paper by D. Yakubovich a new similarity model for a class of Toeplitz operators is constructed. S. Treil' presents a survey of a part of spectral function theory for vector valued function (Szego-Kolmogorov extreme prob!ems for operator weights, bases of vector rational functions, estimations of Hilbert transform with respect to operator weights, the operator corona problem). As a concluding remark I dare only note that the whole collection convinces us once more without a doubt of the fruitfullness of the natural union of operator theory and complex analysis (if at all the union of these fields is at all different from their intersection).
Toeplitz Matrices And Operators
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Author : Nikolaï Nikolski
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-02
Toeplitz Matrices And Operators written by Nikolaï Nikolski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-02 with Mathematics categories.
A friendly introduction to Toeplitz theory and its applications throughout modern functional analysis.
A Short Course On Spectral Theory
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Author : William Arveson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
A Short Course On Spectral Theory written by William Arveson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Mathematics categories.
This book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators on infinite-dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra; the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C-algebras being three areas of current research activity that require mastery of the material presented here. The notion of spectrum of an operator is based on the more abstract notion of the spectrum of an element of a complex Banach algebra. After working out these fundamentals we turn to more concrete problems of computing spectra of operators of various types. For normal operators, this amounts to a treatment of the spectral theorem. Integral operators require 2 the development of the Riesz theory of compact operators and the ideal L of Hilbert–Schmidt operators. Toeplitz operators require several important tools; in order to calculate the spectra of Toeplitz operators with continuous symbol one needs to know the theory of Fredholm operators and index, the ? structure of the Toeplitz C-algebra and its connection with the topology of curves, and the index theorem for continuous symbols.
Spectral Theory Of Differential Operators
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Author : T. Suslina
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-01-01
Spectral Theory Of Differential Operators written by T. Suslina and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
Translations of articles on mathematics appearing in various Russian mathematical serials.
Spectral Properties Of Banded Toeplitz Matrices
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Author : Albrecht Boettcher
language : en
Publisher: SIAM
Release Date : 2005-01-01
Spectral Properties Of Banded Toeplitz Matrices written by Albrecht Boettcher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
This self-contained introduction to the behavior of several spectral characteristics of large Toeplitz band matrices is the first systematic presentation of a relatively large body of knowledge. Covering everything from classic results to the most recent developments, Spectral Properties of Banded Toeplitz Matrices is an important resource. The spectral characteristics include determinants, eigenvalues and eigenvectors, pseudospectra and pseudomodes, singular values, norms, and condition numbers. Toeplitz matrices emerge in many applications and the literature on them is immense. They remain an active field of research with many facets, and the material on banded ones until now has primarily been found in research papers.