John Garnett: Bounded Analytic Functions

Cover: 9781441922168 | Bounded Analytic Functions | John Garnett | Taschenbuch | xiv | 2010

Rückseite: 9781441922168 | Bounded Analytic Functions | John Garnett | Taschenbuch | xiv | 2010

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Sprache: Englisch

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Beschreibung

"This book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The last seven of the ten chapters are devoted in the main to these recent developments. The motif of the theory of Hardy spaces is the interplay between real, complex, and abstract analysis. While paying proper attention to each of the three aspects, the author has underscored the effectiveness of the methods coming from real analysis, many of them developed as part of a program to extend the theory to Euclidean spaces, where the complex methods are not available...Each chapter ends with a section called Notes and another called Exercises and further results. The former sections contain brief historical comments and direct the reader to the original sources for the material in the text."

Donald Sarason, MathSciNet

"The book, which covers a wide range of beautiful topics in analysis, is extremely well organized and well written, with elegant, detailed proofs."

From the citation for the AMS Steele Prize for exposition

Zusammenfassung

This book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The book covers a wide range of topics in analysis. It is extremely well organized and well written, with elegant, detailed proofs. Each chapter ends with a section called Notes and another called Exercises and further results. The former sections contain brief historical comments and direct the reader to the original sources for the material in the text. The last seven of the ten chapters are devoted in the main to recent developments. The motif of the theory of Hardy spaces is the interplay between real, complex, and abstract analysis. While paying proper attention to each of the three aspects, the author has underscored the effectiveness of the methods coming from real analysis, many of them developed as part of a program to extend the theory to Euclidean spaces, where the complex methods are not available.

Inhaltsverzeichnis

Preliminaries.- Hp Spaces.- Conjugate Functions.- Some Extremal Problems.- Some Uniform Algebra.- Bounded Mean Oscillation.- Interpolating Sequences.- The Corona Construction.- Douglas Algebras.- Interpolating Sequences and Maximal Ideals.

Erscheinungsjahr:	2010
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiv 463 S. 31 s/w Illustr. 463 p. 31 illus.
ISBN-13:	9781441922168
ISBN-10:	1441922164
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Garnett, John
Auflage:	Softcover reprint of hardcover 1st edition 2007
Hersteller:	Springer US Springer New York Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	229 x 152 x 26 mm
Von/Mit:	John Garnett
Erscheinungsdatum:	19.11.2010
Gewicht:	0,683 kg

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