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)...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171284000594 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |