Nikolai Nikolski

Hardy Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 31. Januar 2019
• Englisch
• ISBN-13: 9781316886830
• Artikelnr.: 55120646

Autorenporträt

Nikolaï Nikolski is Professor Emeritus at the Université 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 Ampère of the French Academy of Sciences in 2010.

Inhaltsangabe

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.