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Conditionally-periodic function

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A function which is the composition of a -periodic function , where is the -dimensional torus, and a function such that , where is a constant vector whose components are linearly independent over the rational numbers. Examples of conditionally-periodic functions are given by partial sums of Fourier series

where

If a conditionally-periodic function is continuous, then it coincides with a quasi-periodic function with periods .

References

[1] V.I. Arnol'd, "Chapitres supplémentaires de la théorie des équations différentielles ordinaires" , MIR (1980) (Translated from Russian)


Comments

A conditionally-periodic function is almost periodic, cf. Almost-periodic function.

How to Cite This Entry:
Conditionally-periodic function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conditionally-periodic_function&oldid=46445
This article was adapted from an original article by Yu.V. Komlenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article