Hardy Spaces

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.

• 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.

'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