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42: Fourier analysis


Introduction

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.

History

Applications and related fields

[Schematic of subareas and related areas]

Subfields

Browse all (old) classifications for this area at the AMS.


Textbooks, reference works, and tutorials

Software and tables

Other web sites with this focus

Web Resources for Harmonic Analysis (Terry Tao).

Selected Topics at this site


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Last modified 2000/01/14 by Dave Rusin. Mail: