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Pseudo-periodic function

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with periods

A function of variables satisfying:

Example: if and are continuous periodic functions with periods and , respectively, then is a pseudo-periodic function.

A pseudo-periodic function is connected with a quasi-periodic function and is determined by it in a unique way: A function is quasi-periodic with periods if and only if there exists a continuous pseudo-periodic function with periods such that .


Comments

The expression "pseudo-periodic function" is also used to indicate a function with a pseudo--period: for some and all . For such a function the function is pseudo-periodic in the sense above.

References

[a1] M. Urabe, "Green functions of pseudo-periodic differential operators" M. Urabe (ed.) , Japan-United States Sem. Ordinary Differential and Functional Eq. , Springer (1971) pp. 106–122
[a2] J.A. Goldstein, "Asymptotics for bounded semigroups on Hilbert space" R. Nagel (ed.) et al. (ed.) , Aspects of Positivity in Funct. Anal. , North-Holland (1986) pp. 49–62
How to Cite This Entry:
Pseudo-periodic function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pseudo-periodic_function&oldid=48350
This article was adapted from an original article by Yu.V. Komlenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article