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Cambridge Studies in Advanced Mathematics
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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; References; Notation; Index.

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Graduate text covering the theory of Hardy spaces from its origins to the present, with concrete applications and solved exercises.

About the Author

Nikolai Nikolski is Professor Emeritus at the Universite de Bordeaux working primarily in analysis and operator theory. He has been co-editor of four international journals and published numerous articles and research monographs. He has also supervised some thirty Ph.D. students, including three Salem Prize winners. Professor Nikolski was elected Fellow of the American Mathematical Society (AMS) in 2013 and received the Prix Ampere of the French Academy of Sciences in 2010.

Reviews

Advance praise: '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 Louis
Advance praise: '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 Autonoma de Barcelona
Advance praise: '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
Advance praise: 'From the high stand due to a lifelong affinity for the subject, Nikolai 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
Advance praise: '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 Louis
Advance praise: '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 Autonoma de Barcelona
Advance praise: '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
Advance praise: 'From the high stand due to a lifelong affinity for the subject, Nikolai 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

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