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Fourier Analysis

4.3 out of 5 stars 9 customer reviews
ISBN-13: 978-0521389914
ISBN-10: 0521389917
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Editorial Reviews

Review

"...an extraordinary and very attractive book...I would like to see the book on the desk of every pure mathematician with an interest in analysis, and of every teacher of applied mathematics whose work involves analysis."
SIAM Review

"This book is a delight because of the author's informal style (even the index is fun to read), his wide knowledge and skillful exposition, and his insights into many different topics (which come from problems in the real world)."
The UMAP Journal

"...deserves to be widely read...experts will read it for enjoyment, non-experts for instruction..."
D.L. Salinger, London Math Society

"A stimulating survey of the ideas, techniques, and elegant results to be obtained from Fourier analysis...will be welcomed by all who want more than a basic account of the subject."
Sci-Tech Book News

"This book is that rare delight: a serious mathematical book that is thoroughly enjoyable throughout: one can read it almost as easily as a novel and it is diffucult to put down--one is continually tempted to find out 'what happens next'...the book is accessible to a good second-year undergraduate with a taste for analysis. Anyone who wants to find out what Fourier analysis can do would enjoy looking into it."
The Mathematical Gazette

"...a very attractive book which certainly merits its place beside the vast amount of literature on Fourier theory that already exists...it is certainly worthwhile trying to persuade your library to buy it."
M. Zwaan, Acta Applicandae Mathematicae

"This is a wonderful book. More than anything, this is just fun to read, to browse, to study. Fourier Analysis is literate, lively, and a true classic. I highly recommend it."
Bill Satzer, MAA Reviews

Book Description

Ranging from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering, the techniques and results of Fourier analysis and applications are displayed in perspective.
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Product Details

  • Paperback: 591 pages
  • Publisher: Cambridge University Press (November 24, 1989)
  • Language: English
  • ISBN-10: 0521389917
  • ISBN-13: 978-0521389914
  • Product Dimensions: 6.8 x 1.2 x 9.7 inches
  • Shipping Weight: 2.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #345,555 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback
This book is valuable for its emphasis on interesting applications. The treatment of the mathematical basics of Fourier analysis is too hasty to be of much value as a first text, but this is only to leave room for the many beautiful applications. To set the tone, Weyl's equidistribution theorem appears on page 11 (sic). Later we see the classical problems of 19th century physics, but also little samples of Brownian motion, Monte Carlo methods, cryptography and other modern things. When Korner feels like it, he includes historical remarks and anecdotes that are pleasantly told. I wish this cosy atmosphere could also have been upheld in the mathematical details. Unfortunately, when it comes to the proofs, Korner seems to have a bit of a macho attitude towards long calculations. A few words of explanation here and there would probably be of great help when one is lost in page after page of technical lemmas consisting of nothing but formulas and curious integral approximations.
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Format: Paperback
I am a physician though I was a math grad student at MIT for 5 years a long time ago. I found this a wonderful book for reading and working though in spare time. I used to think of Fourier Series as engineering stuff so I was surprized to find Dedekind's theorem on primes in arithmetic progressions and Weyl's on the distribution of integral multiples of an irrational modulo 1. Korner succeeded in giving me an entirely new outlook on harmonic analysis as well as some new perspectives on surprizing, incident areas of math.
In addition, he is a fine writer. I would put him up with Halmos in quality though a very different style.
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Format: Paperback
This book makes great reading. There is a fair amount of (well written) high level mathematics, but also a number of sections of a more historical or narrative nature, and a wonderful sense of humor pervades the work. The account of the laying of the transatlantic cable in the nineteenth century and the technical problems associated with it is priceless. Several sections are devoted to the life of Fourier. There is also a companion volume entitled ``Exercises for Fourier analysis''.
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Format: Paperback
The author weaves together stories, application, and mathematics to give a fairly complete vision of Fourier analysis. All the mathematics is done without requiring measure theory, and the motivation is always in the forefront. My personal favorite parts are the on the building of the transatlantic cable and the example of outstanding statististical analysis. Make sure to purchase the exercises book, even if it is only for the jokes.
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Format: Paperback
Writing a book on Fourier theory is fraught with problems simply because of the technical difficulty of the subject and the enormous scope of applications. The 19th century roots of the theory were highly analytical and revolved around ever more subtle issues of convergence which persisted even until 1966, culminating with Lennart Carelson's famous proof. Applied mathematicians have used Fourier theory as a daily tool for many years without worrying too much about subtle convergence properties, Schwartz spaces and so on. Indeed, Fourier theory figured in the discovery of DNA. In fact Fourier theory is everywhere and Tom Korner's book gives a real flavour of how far its tentacles extend. His chapters on the transatlantic cable, the diameter of stars, the age of the earth, Brownian motion, scientific fraud and more of are considerable interest and it is not often that one finds so much relevant historical material thrown into a mathematical tract. But that is Tom Korner.

For those who aren't aware, Korner is a Cambridge mathematician who has spent his life specialising in Fourier theory. He also has a sense of humour. He is fond of finding counter examples in analysis and those who have read his lecture notes (check out his website) will know exactly what I mean. He takes you to the edge and gently pushes you over with a smile. He brings a classical analysts' approach to Fourier analysis as a subject which also cross-dresses as a highly applied discipline. It is possible to do electrical engineering courses without knowing all the subtleties that give hard core Fourier analysts a stirring in their mathematical loins.
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