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Fourier coefficients of an almost-periodic function

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The coefficients of the Fourier series (cf. Fourier series of an almost-periodic function) corresponding to the given almost-periodic function :

where

The coefficients are completely determined by the theorem on the existence of the mean value

which is non-zero only for the countable set of values .


Comments

References

[a1] A.S. Besicovitch, "Almost periodic functions" , Cambridge Univ. Press (1932) pp. Chapt. I
[a2] N. Wiener, "The Fourier integral and certain of its applications" , Dover, reprint (1933) pp. Chapt. II
How to Cite This Entry:
Fourier coefficients of an almost-periodic function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fourier_coefficients_of_an_almost-periodic_function&oldid=32626
This article was adapted from an original article by E.A. Bredikhina (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article