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

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  • Gaston Mandata N'Guerekata

Abstract

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.

Suggested Citation

  • Gaston Mandata N'Guerekata, 1984. "Almost-periodicity in linear topological spaces and applications to abstract differential equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 7, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:891546
    DOI: 10.1155/S0161171284000594
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