FOURIER SERIES

Abstract 

Fourier series has long provided one of the principal methods 
of analysis for mathematical physics, engineering, and signal
processing.  It has spurred generalizations and applications 
that continue to develop right up to the present.  While the 
original theory of Fourier series applies to periodic
functions occurring in wave motion, such as with light and 
sound, its generalizations often relate to wider settings, 
such as the time-frequency analysis underlying the recent 
theories of wavelet analysis and local trigonometric
analysis.

There are nine sections to this article, they are:

I.  Introduction
II.  Historical background
III.  Definition of Fourier series
IV.  Convergence of Fourier series
V.  Convergence in norm
VI.  Summability of Fourier series
VII.  Generalized Fourier series
VIII.  Discrete Fourier series
IX.  Conclusion