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Distributions pp 237-270 | Cite as

Fourier Series

  • J. J. Duistermaat
  • J. A. C. Kolk
Chapter
Part of the Cornerstones book series (COR)

Abstract

The theory of Fourier series is a far-reaching analog of writing \(x \in \mathbf {\rm R}^n {\rm{as}}\ x = \sum\limits_{j = 1}^n {\left\langle {x,e_j } \right\rangle } e_j,\) the decomposition of a vector into a sum of projections along the vectors e j, which form a complete system of orthonormal vectors \((e_1,...,e_n )\ {\rm in\ \mathbf R}^n.\)

Keywords

Fourier Series Moderate Growth Summation Formula Poisson Kernel Periodic Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematical InstituteUtrecht UniversityUtrechtThe Netherlands

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