An Introduction to Harmonic Analysis

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Cambridge University Press, 2004 - Mathematics - 314 pages
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First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.
 

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Contents

Fourier Series on T page
1
The Convergence of Fourier Series
67
The Conjugate Function
83
Interpolation of Linear Operators
117
Lacunary Series and Quasianalytic Classes
133
Fourier Transforms on the Line
151
Fourier Analysis on Locally Compact Abelian Groups
223
Commutative Banach Algebras
231
VectorValued Functions
295
B Probabilistic Methods
299
Bibliography
307
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About the author (2004)

Yitzhak Katznelson received his Ph.D. from the University of Paris. He is currently a Professor of mathematics at Stanford University, and has also taught at University of C alifornia, Berkeley, Hebrew University andYale University. His mathematical interests include harmonic analysis, ergodic theory, and differentiable dyamics

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