Commutative Harmonic Analysis I: General Survey Classical Aspects

First American Edition (1991) . Near Fine: a tiny soil spot at the lower front panel and the very mildest nudges to the upper corner tips; faint soiling to the panels; else flawless; the binding is square and secure; the text is clean. Free of creased or dog-eared pages in the text. Free of any underlining, hi-lighting or marginalia or marks in the text. Free of ownership names, dates, addresses, notations, inscriptions, stamps, or labels. A handsome copy, structurally sound and tightly bound, showing minor, unobtrusive imperfections. Remains bright and clean. NOT a Remainder, Book-Club, or Ex-Library. 8vo (9.5 x 6.25 x 0.75 inches) . Language: English. Weight: 20.4 ounces. Yellow cloth over boards with dark blue titles at the front panel and backstrip. This text was first published in Russian in 1987. Hardcover: No DJ as issued. 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. ; Encyclopaedias of Mathematical Sciences; Vol. 15; Large 8vo 9" - 10" tall; vi, 268 pages. …