Cover image for Fourier analysis
Title:
Fourier analysis
Author:
Körner, T. W. (Thomas William), 1946-
Publication Information:
Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1989.

©1988
Physical Description:
xii, 591 pages : illustrations ; 26 cm
General Note:
Includes index.
Language:
English
Subject Term:
ISBN:
9780521251204
Format :
Book

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QA403.5 .K67 1988 Adult Non-Fiction Non-Fiction Area
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Summary

Summary

The author has provided a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy, and electrical engineering. Each application is placed in perspective with a short essay. The prerequisites are few (the reader with knowledge of second or third year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining.


Reviews 1

Choice Review

A marvelous book that should be in every serious academic library. It explores at a high but "elementary" level (i.e., avoiding Lebesgue integrals) the field of analysis that has given rise to much of modern mathematics. Korner has written brilliantly 105 short excursions into developments and applications of Fourier analysis, as well as pieces on the nature and history of 19th century science. If the intense mathematical content did not prohibit it, the book could be called a collection of essays. Much of the flavor is historical and scholarly, but many of the topics are decidedly contemporary (RSA ciphers, computer calculation of Fourier transforms). The book, which is more an invitation to individual study than a reference work, is simultaneously an entirely serious and tremendously humorous book. There are several standard works on Fourier analysis (Y. Katznelson's Introduction to Harmonic Analysis, CH, Aug '68, and R.E. Edwards's Fourier Series; A Modern Introduction, 2nd ed., 1979) but they are for the more advanced reader. The only works accessible to undergraduates are dull compared to Korner. The only criticism that might be leveled at the author is the accusation of sexist writing--he invariably refers to the reader as "she." Highly recommended. -S. Puckette, University of the South


Table of Contents

Preface
1 Fourier series
2 Some differential equations
3 Orthogonal series
4 Fourier transforms
5 Further developments
6 Other directions
Appendices
Index