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

Let E be a complete locally convex space (l.c.s.) and f : R → E 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 ℓ = ℓ ( U ) > 0 such that every interval [ a , a + ℓ ] of the real line contains at least one τ point such that f ( t + τ ) − f ( t ) ∈ U for every t ∈ R . We prove in this paper many useful properties of a.p. functions in l.c.s, and give Bochner′s criteria in Fréchet spaces.

Abstract licence: CC BY

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.