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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Fourier Series on T page
The Convergence of Fourier Series
The Conjugate Function
Interpolation of Linear Operators
Lacunary Series and Quasianalytic Classes
Fourier Transforms on the Line
Fourier Analysis on Locally Compact Abelian Groups
Commutative Banach Algebras
VectorValued Functions
B Probabilistic Methods

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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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