Slowly oscillating solutions of Cauchy problems with countable spectrum
Let u be a bounded slowly oscillating mild solution of an inhomogeneous Cauchy problem, u̇(t) = Au(t) + f(t), on ℝ or ℝ+, where A is a closed operator such that σap(A) ∩ iℝ is countable, and the Carleman or Laplace transform of f has a continuous extension to an open subset of the imaginary axis wit...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2000
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| _version_ | 1797062712504614912 |
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| author | Arendt, W Batty, C |
| author_facet | Arendt, W Batty, C |
| author_sort | Arendt, W |
| collection | OXFORD |
| description | Let u be a bounded slowly oscillating mild solution of an inhomogeneous Cauchy problem, u̇(t) = Au(t) + f(t), on ℝ or ℝ+, where A is a closed operator such that σap(A) ∩ iℝ is countable, and the Carleman or Laplace transform of f has a continuous extension to an open subset of the imaginary axis with countable complement. It is shown that u is (asymptotically) almost periodic if u is totally ergodic (or if X does not contain c0 in the case of a problem on ℝ). Similar results hold for second-order Cauchy problems and Volterra equations. |
| first_indexed | 2024-03-06T20:49:29Z |
| format | Journal article |
| id | oxford-uuid:3717bbb1-f506-4ba4-b48b-c622c5846739 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:49:29Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:3717bbb1-f506-4ba4-b48b-c622c58467392022-03-26T13:41:50ZSlowly oscillating solutions of Cauchy problems with countable spectrumJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3717bbb1-f506-4ba4-b48b-c622c5846739EnglishSymplectic Elements at Oxford2000Arendt, WBatty, CLet u be a bounded slowly oscillating mild solution of an inhomogeneous Cauchy problem, u̇(t) = Au(t) + f(t), on ℝ or ℝ+, where A is a closed operator such that σap(A) ∩ iℝ is countable, and the Carleman or Laplace transform of f has a continuous extension to an open subset of the imaginary axis with countable complement. It is shown that u is (asymptotically) almost periodic if u is totally ergodic (or if X does not contain c0 in the case of a problem on ℝ). Similar results hold for second-order Cauchy problems and Volterra equations. |
| spellingShingle | Arendt, W Batty, C Slowly oscillating solutions of Cauchy problems with countable spectrum |
| title | Slowly oscillating solutions of Cauchy problems with countable spectrum |
| title_full | Slowly oscillating solutions of Cauchy problems with countable spectrum |
| title_fullStr | Slowly oscillating solutions of Cauchy problems with countable spectrum |
| title_full_unstemmed | Slowly oscillating solutions of Cauchy problems with countable spectrum |
| title_short | Slowly oscillating solutions of Cauchy problems with countable spectrum |
| title_sort | slowly oscillating solutions of cauchy problems with countable spectrum |
| work_keys_str_mv | AT arendtw slowlyoscillatingsolutionsofcauchyproblemswithcountablespectrum AT battyc slowlyoscillatingsolutionsofcauchyproblemswithcountablespectrum |