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An Introduction to Operators on the Hardy-Hilbert Space (Graduate Texts in Mathematics, 237) - Softcover
Synopsis
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.
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From the Back Cover
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.
Review
From the reviews:
"This text appears as number 237 in the Graduate Texts in Mathematics series published by Springer. ... possible textbook for graduate courses, as well as independent study and reference for research. The book is very well written and contains very elegant proofs. ... Each chapter in the book has plenty of exercises ... . In short: this is a wonderful book, a pleasure to read and use as a text, or add to any mathematician’s ‘collection’ of references to a beautiful and rich subject." (Mihaela Poplicher, MathDL, April, 2007)
"The aim of this book is to provide an introduction to operator theory on the Hardy space H2, also called the Hardy-Hilbert space. ... Each chapter ends with a list of exercises and notes and remarks. ... The book gives an elementary and brief account of some basic aspects of operators on H2 and can be used as a first introduction to this area." (Takahiko Nakazi, Mathematical Reviews, 2007 k)
"This text is a gentle introduction to the ‘concrete’ operator theory on the Hardy-Hilbert space H2, an important model space for operator theory on function spaces. ... Each chapter contains a number of exercises. ... Historical notes and remarks are also included. The bibliography is exhaustive and up to date. The book seems completely suitable for a first- or second-year graduate course in function spaces and operator theory ... and can probably be adapted to both a basic and a more advanced course." (Dragan Vukotic, Zentralblatt MATH, Vol. 1116 (18), 2007)
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- PublisherSpringer
- Publication date2010
- ISBN 10 1441922539
- ISBN 13 9781441922533
- BindingPaperback
- LanguageEnglish
- Number of pages232
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An Introduction to Operators on the Hardy-Hilbert Space
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 236 pp. Englisch. Seller Inventory # 9781441922533
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An Introduction to Operators on the Hardy-Hilbert Space
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An Introduction to Operators on the Hardy-Hilbert Space
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - The great mathematician G. H. Hardy told us that 'Beauty is the rst test: there is no permanent place in the world for ugly mathematics' (see [24, p. 85]). It is clear why Hardy loved complex analysis: it is a very beautiful partofclassicalmathematics. ThetheoryofHilbertspacesandofoperatorson themisalmostasclassicalandisperhapsasbeautifulascomplexanalysis. The studyoftheHardy-Hilbertspace(aHilbertspacewhoseelementsareanalyt ic functions), and of operators on that space, combines these two subjects. The interplay produces a number of extraordinarily elegant results. For example, very elementary concepts from Hilbert space provide simple proofs of the Poisson integral (Theorem 1. 1. 21 below) and Cauchy integral (Theorem 1. 1. 19) formulas. The fundamental theorem about zeros of fu- tions in the Hardy-Hilbert space (Corollary 2. 4. 10) is the central ingredient of a beautiful proof that every continuous function on [0,1] can be uniformly approximated by polynomials with prime exponents (Corollary 2. 5. 3). The Hardy-Hilbert space context is necessary to understand the structure of the invariant subspaces of the unilateral shift (Theorem 2. 2. 12). Conversely, pr- erties of the unilateral shift operator are useful in obtaining results on f- torizations of analytic functions (e. g. , Theorem 2. 3. 4) and on other aspects of analytic functions (e. g. , Theorem 2. 3. 3). The study of Toeplitz operators on the Hardy-Hilbert space is the most natural way of deriving many of the properties of classical Toeplitz mat- ces (e. g. , Theorem 3. 3. Seller Inventory # 9781441922533
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. More elementary than the competitionContains clear and beautiful proofsHas been class-tested a number of timesThis book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a f. Seller Inventory # 4172780
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