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Titlebook: Bounded Analytic Functions; John B. Garnett Textbook 2007 Springer-Verlag New York 2007 algebra.analytic function.function.proof

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发表于 2025-3-21 19:22:35 | 显示全部楼层 |阅读模式
期刊全称Bounded Analytic Functions
影响因子2023John B. Garnett
视频video
发行地址Covers a wide range of beautiful topics in analysis.Well-organized with detailed proofs.Contains numerous exercises and motivation
学科分类Graduate Texts in Mathematics
图书封面Titlebook: Bounded Analytic Functions;  John B. Garnett Textbook 2007 Springer-Verlag New York 2007 algebra.analytic function.function.proof
影响因子."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.
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Lukács’s Phenomenology of Capitalism employs analyticity in a decisiveway. Then we take up Carleson’s original proof. It consists of a geometric construction that has led to many of the deeper results in this theory and that applies to harmonic functions and to more general situations.
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Textbook 2007 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.
发表于 2025-3-22 17:42:57 | 显示全部楼层
The Corona Construction,roof have proved useful for other problems. We first give T.Wolff’s recent, very elegant proof, which is based on Littlewood–Paley integrals and which employs analyticity in a decisiveway. Then we take up Carleson’s original proof. It consists of a geometric construction that has led to many of the
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Self-consciousness and Identityre very pleasing esthetically, and the proofs present an interesting blend of the concrete and the abstract. The corona construction and the BMO duality proof from Chapter VI provide the hard techniques, but the theory of maximal ideals holds the proof together.
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