An Introduction to Harmonic Analysis [Paperback]

A reissue of a classic text on a central topic.First published in 1968, this Introduction has firmly established itself as a classic text and a favorite for students and experts alike. Yitzhak Katznelson begins with an exposition of classical Fourier series. His aim is to demonstrate the central ideas of harmonic analysis and provide a stock of examples to foster a clear understanding of the theory. This new edition has been revised to include several new sections and a new appendix.First published in 1968, this Introduction has firmly established itself as a classic text and a favorite for students and experts alike. Yitzhak Katznelson begins with an exposition of classical Fourier series. His aim is to demonstrate the central ideas of harmonic analysis and provide a stock of examples to foster a clear understanding of the theory. This new edition has been revised to include several new sections and a new appendix.Awarded the American Mathematical Society Steele Prize for Mathematical Exposition, this Introduction, first published in 1968, has firmly established itself as a classic text. Yitzhak Katznelson demonstrates the central ideas of harmonic analysis and provides a stock of examples to foster a clear understanding of the theory. This new edition has been revised to include several new sections and a new appendix.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. Katznelson's An Introduction to Harmonic Analysis is, of course, a classic...So the first thing to say is 'thank you,' to Cambridge for doing this new edition, and to Prof. Katznelson for undertaking the task of updating his book...It is an ambitious book, moving all the way from Fourier series to Banach all*