# Fourier coefficients

From Encyclopedia of Mathematics

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 (*).

#### References

[1] | S. Kaczmarz, H. Steinhaus, "Theorie der Orthogonalreihen" , Chelsea, reprint (1951) |

**How to Cite This Entry:**

Fourier coefficients.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Fourier_coefficients&oldid=17816

This article was adapted from an original article by T.P. Lukashenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article