Fourier analysis studies approximations and
decompositions of functions using trigonometric polynomials. Of incalculable
value in many applications of analysis, this field has grown to include
many specific and powerful results, including convergence criteria,
estimates and inequalities, and existence and uniqueness results.
Extensions include the theory of singular integrals, Fourier transforms,
and the study of the appropriate function spaces. This heading also
includes approximations by other orthogonal families of functions, including
orthogonal polynomials and wavelets.
- 42A: Fourier analysis in one variable
- 42B: Fourier analysis in several variables, For automorphic theory, see mainly 11F30
- 42C: Nontrigonometric Fourier analysis
Browse all (old) classifications for this area at the AMS.
Strichartz, Robert S.: "A guide to distribution theory and Fourier transforms",
Studies in Advanced Mathematics.
CRC Press, Boca Raton, FL, 1994. x+213 pp. ISBN 0-8493-8273-4 MR95f:42001
- Online introduction on Fourier analysis [Forrest Hoffman]
- Kaiser, Gerald: "A friendly guide to wavelets",
Birkhäuser Boston, Inc., Boston, MA, 1994. 300 pp. ISBN 0-8176-3711-7 MR95i:94003
- Online tutorials on wavelets by
- There is a SIAM Activity Group on Orthogonal Polynomials and Special Functions. Their
web site points to the OP-SF NET (electronic newsletter), preprint servers,
and other professional concerns.
- The Wavelet Digest has a home page
with back issues and related links.
- Duhamel, P.; Vetterli, M.:
"Fast Fourier transforms: a tutorial review and a state of the art",
Signal Process. 19 (1990), no. 4, 259--299. MR91a:94004
Web Resources for Harmonic Analysis (Terry Tao).
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Last modified 2000/01/14 by Dave Rusin. Mail: