On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces
We consider abstract differential equations of the form u′(t)=Au(t)+f(t) or u″(t)=Au(t)+f(t) in Banach spaces X, where f(⋅), ℝ→X is almost-periodic, while A is a linear operator, 𝒟(A)⊂X→X. If the solution u(⋅) is likewise almost-periodic, ℝ→X, we establish connections between their Bohr-transforms,...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201012352 |
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| _version_ | 1850166899687555072 |
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| author | Samuel Zaidman |
| author_facet | Samuel Zaidman |
| author_sort | Samuel Zaidman |
| collection | DOAJ |
| description | We consider abstract differential equations of the form u′(t)=Au(t)+f(t) or u″(t)=Au(t)+f(t) in Banach spaces X, where f(⋅), ℝ→X is almost-periodic, while A is a linear operator, 𝒟(A)⊂X→X. If the solution u(⋅) is likewise almost-periodic, ℝ→X, we establish connections between their Bohr-transforms, uˆ(λ) and fˆ(λ). |
| format | Article |
| id | doaj-art-e4e441c1a0474c64a9a3ea55c8477491 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e4e441c1a0474c64a9a3ea55c84774912025-08-20T02:21:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127952153410.1155/S0161171201012352On the Bohr transform of almost-periodic solutions for some differential equations in abstract spacesSamuel Zaidman0Départment de Mathématique et de Statistique, Université de Montréal, Montréal H3C 3J7, QC, CanadaWe consider abstract differential equations of the form u′(t)=Au(t)+f(t) or u″(t)=Au(t)+f(t) in Banach spaces X, where f(⋅), ℝ→X is almost-periodic, while A is a linear operator, 𝒟(A)⊂X→X. If the solution u(⋅) is likewise almost-periodic, ℝ→X, we establish connections between their Bohr-transforms, uˆ(λ) and fˆ(λ).http://dx.doi.org/10.1155/S0161171201012352 |
| spellingShingle | Samuel Zaidman On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces International Journal of Mathematics and Mathematical Sciences |
| title | On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces |
| title_full | On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces |
| title_fullStr | On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces |
| title_full_unstemmed | On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces |
| title_short | On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces |
| title_sort | on the bohr transform of almost periodic solutions for some differential equations in abstract spaces |
| url | http://dx.doi.org/10.1155/S0161171201012352 |
| work_keys_str_mv | AT samuelzaidman onthebohrtransformofalmostperiodicsolutionsforsomedifferentialequationsinabstractspaces |