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Fourier Analysis - Körner, T W
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Every mathematician should have this book. It covers the ideas, techniques and results to be obtained from Fourier Analysis. Also covers applications in number theory, statistics, earth science, astronomy and electrical engineering.

Fourier Analysis 1989, Cambridge University Press, Cambridge

ISBN-13: 9780521389914

Trade paperback

Fourier Analysis 1988, Cambridge University Press, Cambridge, England

ISBN-13: 9780521251204