Commutative Harmonic Analysis - 1: Commutative Harmonic Analysis I

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. Numerous 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.
Dieser Band ist der Anfang der EMS-'Unterreihe' Commutative Harmonic Analysis, in der bisher vier Bände geplant sind. Ein historischer Überblick über Fourieranalysis ist ebenfalls eingeschlossen. Fourieranalysis findet in vielen anderen Fachgebieten der Mathematik Anwendung.

List of contents

I. Methods and Structure of Commutative Harmonic Analysis.- II. Classical Themes of Fourier Analysis.- III. Methods of the Theory of Singular Integrals: Hilbert Transform and Calderón-Zygmund Theory.- Author Index.

Product details

• Authors: E. M. Dyn'kin
• Assisted by: K Nikol'skij (Editor), K Nikol'skij (Editor), V. P. Khavin (Editor), Viktor Petrovich Khavin (Editor), D. Khavinson (Editor), S. V. Kislyakov (Editor), Nikolai Kapitonovich Nikolskij (Editor), N. K. Nikol'skij (Editor), P Khavin (Editor), V P Khavin (Editor), D. Khavinson (Translation), S. V. Kislyakov (Translation)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.01.1960
• EAN: 9783540181804
• ISBN: 978-3-540-18180-4
• No. of pages: 270
• Dimensions: 157 mm x 245 mm x 18 mm
• Weight: 590 g
• Illustrations: X, 270 p.
• Sets: Commutative Harmonic Analysis; Commutative Harmonic Analysis
• Series: Encyclopaedia of Mathematical Sciences; Encyclopaedia of Mathematical Sciences
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra