Nikolʹskiĭ, N. K. creator Nikolʹskiĭ, N. K. text New York :Cambridge University Press 2019 monographic eng

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xviii, 277 pages : illustrations ;24 cm 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. 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 / N K Nikolʹskiĭ Mathematics Analysis Hardy spaces Functions of complex variables Holomorphic functions 515.98 NIK 9781107184541 :Raghav Books Private Limited :A-184 Nand Gram Ghaziabad 210728 20211006163307.0