An Introduction to Operators on the Hardy-Hilbert Space

An Introduction to Operators on the Hardy-Hilbert Space
Title An Introduction to Operators on the Hardy-Hilbert Space PDF eBook
Author Ruben A. Martinez-Avendano
Publisher Springer Science & Business Media
Pages 230
Release 2007-03-12
Genre Mathematics
ISBN 0387485783

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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.

An Introduction to Hilbert Space

An Introduction to Hilbert Space
Title An Introduction to Hilbert Space PDF eBook
Author N. Young
Publisher Cambridge University Press
Pages 254
Release 1988-07-21
Genre Mathematics
ISBN 1107717167

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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.

Hardy Classes and Operator Theory

Hardy Classes and Operator Theory
Title Hardy Classes and Operator Theory PDF eBook
Author Marvin Rosenblum
Publisher Courier Corporation
Pages 204
Release 1997-01-01
Genre Mathematics
ISBN 9780486695365

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Concise treatment focuses on theory of shift operators, Toeplitz operators and Hardy classes of vector- and operator-valued functions. Topics include general theory of shift operators on a Hilbert space, use of lifting theorem to give a unified treatment of interpolation theorems of the Pick-Nevanlinna and Loewner types, more. Appendix. Bibliography. 1985 edition.

An Introduction to Hankel Operators

An Introduction to Hankel Operators
Title An Introduction to Hankel Operators PDF eBook
Author Jonathan R. Partington
Publisher Cambridge University Press
Pages 116
Release 1988
Genre Mathematics
ISBN 9780521367912

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Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.

Operator Theory in Function Spaces

Operator Theory in Function Spaces
Title Operator Theory in Function Spaces PDF eBook
Author Kehe Zhu
Publisher American Mathematical Soc.
Pages 368
Release 2007
Genre Mathematics
ISBN 0821839659

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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.

Operator Analysis

Operator Analysis
Title Operator Analysis PDF eBook
Author Jim Agler
Publisher Cambridge University Press
Pages 393
Release 2020-03-26
Genre Mathematics
ISBN 1108485448

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This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.

Pick Interpolation and Hilbert Function Spaces

Pick Interpolation and Hilbert Function Spaces
Title Pick Interpolation and Hilbert Function Spaces PDF eBook
Author Jim Agler
Publisher American Mathematical Society
Pages 330
Release 2023-02-22
Genre Mathematics
ISBN 1470468557

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The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.