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International Journal of Mathematics and Mathematical Sciences
Volume 7, Issue 3, Pages 529-540
http://dx.doi.org/10.1155/S0161171284000594

Almost-periodicity in linear topological spaces and applications to abstract differential equations

Université de Bangui, Faculté des Sciences, BP 1450 Bangui, Central African Republic

Received 28 April 1982; Revised 10 June 1982

Copyright © 1984 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let E be a complete locally convex space (l.c.s.) and f:RE a continuous function; then f is said to be almost-periodic (a.p.) if, for every neighbourhood (of the origin in E) U, there exists =(U)>0 such that every interval [a,a+] of the real line contains at least one τ point such that f(t+τ)f(t)U for every tR. We prove in this paper many useful properties of a.p. functions in l.c.s, and give Bochner's criteria in Fréchet spaces.