| Document Type
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BL
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| Record Number
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839185
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| Uniform Title
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Élements d'analyse avancée.English
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| Main Entry
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Nikolʹskiĭ, N. K., (Nikolaĭ Kapitonovich)
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| Title & Author
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Hardy spaces /\ Nikolaï Nikolski (Universite de Bordeaux).
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| Publication Statement
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Cambridge ;New York, NY :: Cambridge University Press,, 2019.
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| Series Statement
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Cambridge studies in advanced mathematics ;; 179
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| Page. NO
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xviii, 277 pages :: illustrations ;; 24 cm
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| ISBN
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1107184541
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: 9781107184541
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9781316886830 (PDF ebook)
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| Notes
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First English translation.
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Originally published in French: Élements d'analyse avancée : 1, Espaces de Hardy (Paris : Editions Belin, 2012).
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| Bibliographies/Indexes
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Includes bibliographical references (pages 259-267) and index.
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| Contents
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1. The space H²(T) : an archetypal invariant subspace -- 2. The Hp(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 H² 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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| Abstract
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"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."--Publisher's description.
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| Subject
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Functions of complex variables.
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Hardy spaces.
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Holomorphic functions.
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Functions of complex variables.
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| Subject
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Hardy spaces.
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| Subject
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Holomorphic functions.
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| Dewey Classification
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515/.98
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| LC Classification
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QA331.7.N5513 2019
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