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Author : Jonathan R. Partington
Publisher : Cambridge University Press
Page : 116 pages
File Size : 44,8 Mb
Release : 1988
Category : Mathematics
ISBN : 0521367913
Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
Author : Jonathan R. Partington
Publisher : Unknown
Page : 112 pages
File Size : 49,7 Mb
Release : 1988
Category : Hankel operators
ISBN : 1107366429
Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
Author : Reader in Functional Analysis and Systems Theory School of Mathematics Jonathan R Partington
Publisher : Unknown
Page : 112 pages
File Size : 48,5 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107361516
Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
Author : Vladimir Peller
Publisher : Springer Science & Business Media
Page : 789 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780387216812
The purpose of this book is to describe the theory of Hankel operators, one of the most important classes of operators on spaces of analytic func tions. Hankel operators can be defined as operators having infinite Hankel matrices (i. e. , matrices with entries depending only on the sum of the co ordinates) with respect to some orthonormal basis. Finite matrices with this property were introduced by Hankel, who found interesting algebraic properties of their determinants. One of the first results on infinite Han kel matrices was obtained by Kronecker, who characterized Hankel matri ces of finite rank as those whose entries are Taylor coefficients of rational functions. Since then Hankel operators (or matrices) have found numerous applications in classical problems of analysis, such as moment problems, orthogonal polynomials, etc. Hankel operators admit various useful realizations, such as operators on spaces of analytic functions, integral operators on function spaces on (0,00), operators on sequence spaces. In 1957 Nehari described the bounded Hankel operators on the sequence space £2. This description turned out to be very important and started the contemporary period of the study of Hankel operators. We begin the book with introductory Chapter 1, which defines Hankel operators and presents their basic properties. We consider different realiza tions of Hankel operators and important connections of Hankel operators with the spaces BMa and V MO, Sz. -Nagy-Foais functional model, re producing kernels of the Hardy class H2, moment problems, and Carleson imbedding operators.
Author : Ruben A. Martinez-Avendano,Peter Rosenthal
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 55,8 Mb
Release : 2007-03-12
Category : Mathematics
ISBN : 9780387485782
This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
Author : S. C. Power
Publisher : Pitman Publishing
Page : 112 pages
File Size : 43,5 Mb
Release : 1982
Category : Mathematics
ISBN : UCAL:B4406654
Author : Jonathan R. Partington
Publisher : Cambridge University Press
Page : 184 pages
File Size : 46,9 Mb
Release : 2004-03-15
Category : Mathematics
ISBN : 0521546192
Publisher Description
Author : Sheldon Jay Axler,John E. McCarthy,Donald Sarason
Publisher : Cambridge University Press
Page : 490 pages
File Size : 50,8 Mb
Release : 1998-05-28
Category : Mathematics
ISBN : 0521631939
Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.
Author : N. Young
Publisher : Cambridge University Press
Page : 254 pages
File Size : 47,8 Mb
Release : 1988-07-21
Category : Mathematics
ISBN : 9781107717169
This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.
Author : Peter Harmand,Dirk Werner,Wend Werner
Publisher : Springer
Page : 390 pages
File Size : 42,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540477532
This book provides a comprehensive exposition of M-ideal theory, a branch ofgeometric functional analysis which deals with certain subspaces of Banach spaces arising naturally in many contexts. Starting from the basic definitions the authors discuss a number of examples of M-ideals (e.g. the closed two-sided ideals of C*-algebras) and develop their general theory. Besides, applications to problems from a variety of areas including approximation theory, harmonic analysis, C*-algebra theory and Banach space geometry are presented. The book is mainly intended as a reference volume for researchers working in one of these fields, but it also addresses students at the graduate or postgraduate level. Each of its six chapters is accompanied by a Notes-and-Remarks section which explores further ramifications of the subject and gives detailed references to the literature. An extensive bibliography is included.
Author : Friedrich Haslinger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 298 pages
File Size : 40,7 Mb
Release : 2014-08-20
Category : Mathematics
ISBN : 9783110377835
The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. It begins with results on the canonical solution operator to restricted to Bergman spaces of holomorphic d-bar functions in one and several complex variables.These operators are Hankel operators of special type. In the following the general complex is investigated on d-bar spaces over bounded pseudoconvex domains and on weighted d-bar spaces. The main part is devoted to the spectral analysis of the complex Laplacian and to compactness of the Neumann operator. The last part contains a detailed account of the application of the methods to Schrödinger operators, Pauli and Dirac operators and to Witten-Laplacians. It is assumed that the reader has a basic knowledge of complex analysis, functional analysis and topology. With minimal prerequisites required, this book provides a systematic introduction to an active area of research for both students at a bachelor level and mathematicians.
Author : Nikolaï Nikolski
Publisher : Cambridge University Press
Page : 453 pages
File Size : 42,7 Mb
Release : 2020-01-02
Category : Mathematics
ISBN : 9781107198500
A friendly introduction to Toeplitz theory and its applications throughout modern functional analysis.
Author : Aurelian Gheondea
Publisher : Cambridge University Press
Page : 511 pages
File Size : 42,9 Mb
Release : 2022-07-28
Category : Mathematics
ISBN : 9781108969031
Presents a modern, readable introduction to spaces with indefinite inner product and their operator theory.
Author : Albrecht Böttcher,Bernd Silbermann
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461214267
Applying functional analysis and operator theory to some concrete asymptotic problems of linear algebra, this book contains results on the stability of projection methods, deals with asymptotic inverses and Moore-Penrose inversion of large Toeplitz matrices, and embarks on the asymptotic behaviour of the norms of inverses, the pseudospectra, the singular values, and the eigenvalues of large Toeplitz matrices. The approach is heavily based on Banach algebra techniques and nicely demonstrates the usefulness of C*-algebras and local principles in numerical analysis, including classical topics as well as results and methods from the last few years. Though employing modern tools, the exposition is elementary and points out the mathematical background behind some interesting phenomena encountered with large Toeplitz matrices. Accessible to readers with basic knowledge in functional analysis, the book addresses graduates, teachers, and researchers and should be of interest to everyone who has to deal with infinite matrices (Toeplitz or not) and their large truncations.
Author : Kehe Zhu
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 43,7 Mb
Release : 2007
Category : Function spaces
ISBN : 9780821839652
This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.
