Fourier coefficients

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The coefficients


in the expansion of a function defined on a space with respect to an orthogonal system of real-valued (complex-valued) functions on . If is an orthogonal system in a Hilbert (pre-Hilbert) space, then, given an element of this space, the numbers are also called the Fourier coefficients of with respect to the system . J. Fourier first investigated trigonometric series with coefficients defined by (*).


[1] S. Kaczmarz, H. Steinhaus, "Theorie der Orthogonalreihen" , Chelsea, reprint (1951)
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Fourier coefficients. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by T.P. Lukashenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article