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.
Contents
1. Fourier series on T; 2. The convergence of Fourier series; 3. The conjugate function; 4. Interpolation of linear operators; 5. Lacunary series and quasi-analytic classes; 6. Fourier transforms on the line; 7. Fourier analysis on locally compact Abelian groups; 8. Commutative Banach algebras; A. Vector-valued functions; B. Probabilistic methods.
Review
'… the third, revised, edition … Katznelson managed to improve on a seemingly perfect book!' Nieuw Archif voor Wiskunde
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