- Author: Nikolaï Nikolski, Université de Bordeaux
The theory of Hardy spaces is a cornerstone of modern analysis. It combines techniques from functional analysis, the theory of analytic functions and Lesbesgue integration to create a powerful tool for many applications, pure and applied, from signal processing and Fourier analysis to maximum modulus principles and the Riemann zeta function. This book, aimed at beginning graduate students, introduces and develops the classical results on Hardy spaces and applies them to fundamental concrete problems in analysis. The results are illustrated with numerous solved exercises that also introduce subsidiary topics and recent developments. The reader's understanding of the current state of the field, as well as its history, are further aided by engaging accounts of important contributors and by the surveys of recent advances (with commented reference lists) that end each chapter. Such broad coverage makes this book the ideal source on Hardy spaces.Read more
- A complete introduction to Hardy spaces, including classical results and applications, accounts of the field's history, and surveys of recent developments
- Numerous exercises and solutions illustrate the theory and introduce further applications
- Suitable for beginning graduate students, and includes a concise account of the necessary background from analysis
Reviews & endorsements
'This is a beautiful introduction to a beautiful subject. The author does a masterful job of choosing topics that give a solid introduction to Hardy spaces without overwhelming the reader with too much too soon. Every student of mathematics should enjoy this book.' John McCarthy, Washington University, St LouisSee more reviews
'This is an excellent, highly-recommendable book by a leading expert in the field. Describing in a self-contained way the classical approach to Hardy spaces and their applications - with emphasis on the invariant subspace point of view - it also offers an entertaining journey into the history of twentieth-century analysis.' Joaquim Bruna, Universitat Autònoma de Barcelona
'The author has created a very interesting text that will serve as a source of basic material and an introduction for those interested in the interactions between harmonic analysis, complex analysis, and operator theory. Any researcher who masters the material in this text is well placed to read the more intensive monographs that further develop the interactions of these subjects.' Brett Wick, Washington University, St Louis
'From the high stand due to a lifelong affinity for the subject, Nikolaï Nikolski delineates and recounts the fascinating history of Hardy space with style. His inviting text is sparkled with biographical snapshots, colorful anecdotes, and insightful remarks, conveying a vivid picture of the field. The mathematical discourse is light, yet rigorous and self-contained. Carefully selected problems offer the earnest reader perspectives into current research. The apogee chapter is devoted to the immersion of the daunting Riemann hypothesis into Hardy space framework … Nikolski's text is a truly masterful piece of scholarship.' Mihai Putinar, University of California, Santa Barbara
'This is a comfortably paced introduction to the theory of Hardy spaces, starting at a level of advanced graduate students in analysis … Historical context and biographical details of the main researchers of the field is discussed more deeply than in comparable books.' M. Bona, Choice
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- Date Published: January 2019
- format: Adobe eBook Reader
- isbn: 9781316886830
- contains: 41 b/w illus. 75 exercises
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
The origins of the subject
1. The space H^2(T). An archetypal invariant subspace
2. The H^p(D) classes. Canonical factorization and first applications
3. The Smirnov class D and the maximum principle
4. An introduction to weighted Fourier analysis
5. Harmonic analysis and stationary filtering
6. The Riemann hypothesis, dilations, and H^2 in the Hilbert multi-disk
Appendix A. Key notions of integration
Appendix B. Key notions of complex analysis
Appendix C. Key notions of Hilbert spaces
Appendix D. Key notions of Banach spaces
Appendix E. Key notions of linear operators
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