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Author: Ruben A. Martinez-Avendano
Publisher: Springer Science & Business Media
ISBN: 0387485783
Category : Mathematics
Languages : en
Pages : 230
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Book Description
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: Ruben A. Martinez-Avendano
Publisher: Springer Science & Business Media
ISBN: 0387485783
Category : Mathematics
Languages : en
Pages : 230
Get Book Here
Book Description
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: N. Young
Publisher: Cambridge University Press
ISBN: 1107717167
Category : Mathematics
Languages : en
Pages : 254
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Book Description
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: Ruben A. Martinez-Avendano
Publisher: Springer Science & Business Media
ISBN:
Category : Mathematics
Languages : en
Pages : 248
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Book Description
The subject of this book is operator theory on the Hardy space H2, also called the Hardy-Hilbert space. This is a popular area, partially because the Hardy-Hilbert space is the most natural setting for operator theory. A reader who masters the material covered in this book will have acquired a firm foundation for the study of all spaces of analytic functions and of operators on them. The goal is to provide an elementary and engaging introduction to this subject that will be readable by everyone who has understood introductory courses in complex analysis and in functional analysis. The exposition, blending techniques from "soft" and "hard" analysis, is intended to be as clear and instructive as possible. Many of the proofs are very elegant. This book evolved from a graduate course that was taught at the University of Toronto. It should prove suitable as a textbook for beginning graduate students, or even for well-prepared advanced undergraduates, as well as for independent study. 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: Marvin Rosenblum
Publisher: Courier Corporation
ISBN: 9780486695365
Category : Mathematics
Languages : en
Pages : 204
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Book Description
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.
Author: Jonathan R. Partington
Publisher: Cambridge University Press
ISBN: 9780521367912
Category : Mathematics
Languages : en
Pages : 116
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Book Description
Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
Author: Kehe Zhu
Publisher: American Mathematical Soc.
ISBN: 0821839659
Category : Mathematics
Languages : en
Pages : 368
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Book Description
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.
Author: Jim Agler
Publisher: Cambridge University Press
ISBN: 1108485448
Category : Mathematics
Languages : en
Pages : 393
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Book Description
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.
Author: Joseph A. Ball
Publisher: Cambridge University Press
ISBN: 1009020102
Category : Mathematics
Languages : en
Pages : 440
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Book Description
This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.
Author: V. S. Sunder
Publisher: Springer
ISBN: 9811018162
Category : Mathematics
Languages : en
Pages : 107
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Book Description
The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators.
Author: Jonathan R. Partington
Publisher: Cambridge University Press
ISBN: 0521366119
Category : Mathematics
Languages : en
Pages : 113
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Book Description
Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
