- Series: Princeton Mathematical Series (Book 32)
- Hardcover: 312 pages
- Publisher: Princeton University Press; 1st Ed edition (November 1, 1971)
- Language: English
- ISBN-10: 069108078X
- ISBN-13: 978-0691080789
- Product Dimensions: 6 x 0.8 x 9 inches
- Shipping Weight: 1.2 pounds (View shipping rates and policies)
- Average Customer Review: 2 customer reviews
- Amazon Best Sellers Rank: #1,240,709 in Books (See Top 100 in Books)
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Introduction to Fourier Analysis on Euclidean Spaces. (PMS-32) 1st Ed Edition
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The chapter I like the best is Chapter IV, about rotations and functions on the unit sphere in n-dimensions. This involves radial functions, Bessel functions, homogeneous polynomials. There is a proof of Hecke's identity as Theorem 3.4, which is a formula for the Fourier transform of the product of a homogeneous harmonic polynomial and a Gaussian. I also like Chapter VII, about Fourier series in n variables ("multiple Fourier series").
This book is one component of the Stein trilogy on harmonic analysis (together with "Singular Integrals and Differentiability Properties of Functions" and "Harmonic Analysis", both also reviewed by myself), and as such it must be regarded as an authoritative reference on the subject since Elias Stein and Guido Weiss are two of the leading experts in the field, and the material they selected was taken from their teaching and research experience.
The contents of the book are: The Fourier Transform; Boundary Values of Harmonic Functions; The Theory of H^p Spaces on Tubes; Symmetry Properties of the Fourier Transform; Interpolation of Operators; Singular Integrals and Systems of Conjugate Harmonic Functions; Multiple Fourier Series.
Includes motivation and full explanations for each topic, excercises for each chapter, called "further results", and extensive references. Outstanding printing quality and nice clothbound.
These three volumes should be present in every analyst's library.
Please take a look to the rest of my reviews (just click on my name above).