Fourier Series: v. 1: A Modern Introduction (Athena) - Hardcover

Edwards, R E

Hardcover

ISBN 10: 0030620007 ISBN 13: 9780030620003

Publisher: Holt Rinehart & Winston, 1967

Synopsis

"Modern in method and outlook, this book is suitable for use by a beginner in harmonic analysis or, possibly, in functional analysis and its applications Stress is laid on stome of those aspects of Fourier series that seem to be at the center of current interest and research in harmonic analysis on general groups. Every opportunity has been taken to bring to the reader's notice solved and unsolved problems of which he should be aware. Problems of pointwise convergence and summability are deliberately played down, since they are treated in great detail in other well known workes. Instead, the author emphasizes recently developed and currently favored representation (mean convergence, distributional convergence) as well as structureal problems involving Fourier series of an algebraic-topological nature in various function-spaces (homomorphisms of convolution algebras, multiplier operators). The book offers a self-contained introduction to distributions, measures, and pseudo-measures on the circle group. There is an explanation of how these are related to the problems of spectral synthesis. A distributional treatment of conjugate series is included. A careful discussion of the interpolation theorems of Riesz-Thorin and of Marcinkiewicz, together with some of their most important application to Fourier series, is given. Special attention is paid to the presentation of the Marcinkiewicz theorem, existing accounts of which are too short for a beginner. There is a self-contained introduction to Banach algebras and their major applications to Fourier series. An introductory discussion of closed ideals and closed subalgebras in, and homomorphisms of, varous convolution algebras over the circle group is provided. The book also gives basic standard results about random and lacunary Fourier series and includes a discussion of Sidon sets and their properties. Their continuous analogue, Helson sets, is also discussed."

Edition details

• Publisher: Holt Rinehart & Winston
• Publication date: 1967
• Language: English
• ISBN 10: 0030620007
• ISBN 13: 9780030620003
• Binding: Hardcover
• Edition number: 1
• Number of pages: 208