Commutative Harmonic Analysis I - General Survey: Classical Aspects (Encyclopaedia of Mathematical Sciences) - V. P. Khavin, N. K. Nikol'skij (1991)
ISBN 0387181806
Publisher Springer-Verlag
Publication Date October 1991
Format Hardcover (241 x 165 mm)
This is the first volume in the subseries Commutative Harmonic Analysis of the EMS. It is intended for anyone who wants to get acquainted with the discipline. The first article is a large introduction, also serving as a guide to the rest of the volume. Starting from Fourier analysis of periodic function, then going through the Fourier transform and distributions, the exposition leads the reader to the group theoretic point of view. Numer- rous examples illustrate the connections to differential and integral equations, approximation theory, number theory, probability theory and physics. The article also contains a brief historical essay on the development of Fourier analysis. The second article focuses on some of the classical problems of Fourier series; it's a "mini-Zygmund" for the beginner. In particular, the convergence and summability of Fourier series, translation invariant operators and theorems on Fourier coefficients are given special attention. The third article is the most modern of the three, concentrating on the theory of singular integral operators. The simplest such operator, the Hilbert transform, is covered in detail. There is also a thorough introduction to Calderon-Zygmund theory.
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Collection Status In Collection
Index 725
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Product Details
LoC Classification QA403. K6613 Part I 1991
Cover Price $139.00
No. of Pages 268