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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1849304652791676928 |
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| author | Gaston Mandata N'Guerekata |
| author_facet | Gaston Mandata N'Guerekata |
| author_sort | Gaston Mandata N'Guerekata |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-41a76bcc73d4488eaf739115d04e4ae3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-41a76bcc73d4488eaf739115d04e4ae32025-08-20T03:55:40ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017352954010.1155/S0161171284000594Almost-periodicity in linear topological spaces and applications to abstract differential equationsGaston Mandata N'Guerekata0Université de Bangui, Faculté des Sciences, BP 1450 Bangui, Central African RepublicLet 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.http://dx.doi.org/10.1155/S0161171284000594 |
| spellingShingle | Gaston Mandata N'Guerekata Almost-periodicity in linear topological spaces and applications to abstract differential equations International Journal of Mathematics and Mathematical Sciences |
| title | Almost-periodicity in linear topological spaces and applications to abstract differential equations |
| title_full | Almost-periodicity in linear topological spaces and applications to abstract differential equations |
| title_fullStr | Almost-periodicity in linear topological spaces and applications to abstract differential equations |
| title_full_unstemmed | Almost-periodicity in linear topological spaces and applications to abstract differential equations |
| title_short | Almost-periodicity in linear topological spaces and applications to abstract differential equations |
| title_sort | almost periodicity in linear topological spaces and applications to abstract differential equations |
| url | http://dx.doi.org/10.1155/S0161171284000594 |
| work_keys_str_mv | AT gastonmandatanguerekata almostperiodicityinlineartopologicalspacesandapplicationstoabstractdifferentialequations |