An Introduction to Harmonic Analysis [Paperback]

Yitzhak Katznelson (Author)

Book Description

ISBN-10: 0486633314 | ISBN-13: 978-0486633312 | Publication Date: June 1, 1976 | Edition: 2nd

This concrete approach to harmonic analysis begins with the circle group T and deals with classical Fourier series in the first five chapters, turning to the real line in chapter six, locally compact abelian groups in chapter seven, and commutative Banach algebras in final chapter.

Editorial Reviews

Review

"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 algebras and analysis on locally compact abelian groups. It is densely but clearly written, with the occasional flash of wit."
MAA Reviews, Fernando Q. Gouvea --This text refers to an alternate Paperback edition.

Book Description

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. --This text refers to an alternate Paperback edition.

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Product Details

• Paperback: 264 pages
• Publisher: Dover Publications; 2nd edition (June 1, 1976)
• Language: English
• ISBN-10: 0486633314
• ISBN-13: 978-0486633312
• Product Dimensions: 8.4 x 5.6 x 0.6 inches
• Shipping Weight: 11.7 ounces
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,869,516 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

12 of 12 people found the following review helpful:

5.0 out of 5 stars Still one of the best., April 20, 2003

By 

Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
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This review is from: An Introduction to Harmonic Analysis (Paperback)

When the first edition of Katznelson's book appeared back in 1968 (when I was a student), it soon became the talked about, and universally used, reference volume for the standard tools of harmonic analysis: Fourier series, Fourier transforms, Fourier analysis/synthesis, the math of time-frequency filtering, causality ideas, H^p-spaces, and the various incarnations of Norbert Wiener's ideas on the Fourier transform in the complex domain, Paley-Wiener, spectral theory, and more. It is easy to pick up the essentials in this lovely book. Now, many years later, I occasionaly ask beginning students what their favorite reference is on things like that, and more often than not, it is Katznelson. Thanks to Dover, it is on the shelf of most university bookstores, and priced under US$ 10.

9 of 10 people found the following review helpful:

5.0 out of 5 stars An essential book for anyone studying Harmonic Analysis, May 9, 1998

By A Customer

This review is from: An Introduction to Harmonic Analysis (Paperback)

Katznelson's book considers harmonic analysis primarily on the circle group. He does this from a thorougly modern point of view. An understanding of the basic ideas of Banach spaces is required. This book should be on the shelf of any aspiring Harmonic Analyst, especially one with an abstract viewpoint.

4 of 4 people found the following review helpful:

5.0 out of 5 stars Great Introduction to Classical Harmonic Analysis, March 10, 2000

By 

Pierre (Mexico City) - See all my reviews

This review is from: An Introduction to Harmonic Analysis (Paperback)

This is a great book for looking at classical harmonic analysis: the study of Fourier Series on the "typical" groups, includes a quick look at the general situation and ends with an introduction to commutative Banach Algebras. Both topics are continued in [Loomis].