Nikolski Hardy Spaces

Elements of Advanced Analysis
Erscheinungsjahr 2019
ISBN: 978-1-316-88683-0
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 179, 0 Seiten

Reihe: Cambridge Studies in Advanced Mathematics

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.

Autoren/Hrsg.

Nikolski, Nikolaï

Nikolski, Nikolai

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

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.

Über Autor(innen)

Nikolski, Nikolaï
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.