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A Remark on Integration of Almost-Periodic Functions

Published online by Cambridge University Press:  20 November 2018

S. Zaidman
S. Zaidman*
Affiliation:
Université de Montréal, Montréal, Québec
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A result proved by Favard for scalar-valued almost-periodic functions has an immediate extension to Banach space valued functions (see [2] and [3] for explicit details).

The result says that integrals of almost-periodic functions whose 'spectrum' is at positive distance from 0 are again almost-periodic. Our aim here is to indicate a more general formulation of this result using strongly almost-periodic oneparameter groups of operators in Banach spaces.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 2 , June 1970 , pp. 249 - 251
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Bochner, S., Abstrakte Fast-periodische Funktionen, Acta Math., 1933.Google Scholar
2. Levitan, B. M., Almost-periodic functions, (Russian), Moscow, 1953.Google Scholar
3. Zaidman, S., Solutions presque-périodiques des équations hyperboliques, Ann. Sci. école Norm. Sup., Paris, 1962.Google Scholar
4. Zaidman, S., Sur la perturbation presque-périodique des groupes et semi-groupes de transformations d'un espace de Banach, Rend. Mat. e Appl., Rome, 1957.Google Scholar
5. Gunzler, H. and Zaidman, S., Almost-periodic solutions of a certain abstract differential equation, J. Math. Mech., 1969.Google Scholar