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Fourier Analysis and Its Applications

Gerald B. Folland
Publisher: 
American Mathematical Society
Publication Date: 
2009
Number of Pages: 
433
Format: 
Hardcover
Series: 
Pure and Applied Undergraduate Texts 4
Price: 
72.00
ISBN: 
9780821847909
Category: 
Textbook
[Reviewed by
Allen Stenger
, on
09/17/2009
]

This is a good introductory text to classical harmonic analysis, slanted towards the differential equations that are used in physics. The present volume is a 2009 reprint of the 1992 Wadsworth publication. The book has a good balance of breadth vs. depth: all the major topics are covered, and there is enough depth that you learn something useful and interesting about each topic. There's quite a lot on orthogonal functions, and just a little bit on wavelets and discrete Fourier transforms.

The view of Fourier analysis is broad, and includes Laplace transforms and the use of complex analysis when helpful. For the most part the book does not deal with function spaces, and does not usually make a sharp distinction between L1 and L2 functions. It tiptoes around the Lebesgue integral, hinting (without going into any detail) that there is another kind of integral that is just like the Riemann integral, only much, much better.

Bottom line: a good text for an upper-level undergraduate course, with just the right amount of detail for most students at this level.


Allen Stenger is a math hobbyist, library propagandist, and retired computer programmer. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning. His mathematical interests are number theory and classical analysis.

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