Weighted and local stability of semigroups of operators
We prove global and local weighted stability theorems for representations of abelian semigroups on Banach spaces under countable spectral conditions and certain growth assumptions on the weights. In the global case, we use a limit semigroup construction together with an extension theorem for weighte...
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| Format: | Journal article |
| Language: | English |
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2000
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| _version_ | 1797089139112280064 |
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| author | Batty, C Yeates, S |
| author_facet | Batty, C Yeates, S |
| author_sort | Batty, C |
| collection | OXFORD |
| description | We prove global and local weighted stability theorems for representations of abelian semigroups on Banach spaces under countable spectral conditions and certain growth assumptions on the weights. In the global case, we use a limit semigroup construction together with an extension theorem for weighted semigroup representations. In the local case, we adapt a definition of Albrecht to introduce a local spectrum of a representation which is no larger than the usual notion of local spectrum for representations of Z+ and R+, and we establish the corresponding local stability theorem. We give an application to the asymptotic theory of functions on abelian semigroups. © 2000 Cambridge Philosophical Society. |
| first_indexed | 2024-03-07T03:00:08Z |
| format | Journal article |
| id | oxford-uuid:b0b04e5e-9fe1-45af-9555-89cbd5f50feb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:00:08Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:b0b04e5e-9fe1-45af-9555-89cbd5f50feb2022-03-27T03:58:11ZWeighted and local stability of semigroups of operatorsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b0b04e5e-9fe1-45af-9555-89cbd5f50febEnglishSymplectic Elements at Oxford2000Batty, CYeates, SWe prove global and local weighted stability theorems for representations of abelian semigroups on Banach spaces under countable spectral conditions and certain growth assumptions on the weights. In the global case, we use a limit semigroup construction together with an extension theorem for weighted semigroup representations. In the local case, we adapt a definition of Albrecht to introduce a local spectrum of a representation which is no larger than the usual notion of local spectrum for representations of Z+ and R+, and we establish the corresponding local stability theorem. We give an application to the asymptotic theory of functions on abelian semigroups. © 2000 Cambridge Philosophical Society. |
| spellingShingle | Batty, C Yeates, S Weighted and local stability of semigroups of operators |
| title | Weighted and local stability of semigroups of operators |
| title_full | Weighted and local stability of semigroups of operators |
| title_fullStr | Weighted and local stability of semigroups of operators |
| title_full_unstemmed | Weighted and local stability of semigroups of operators |
| title_short | Weighted and local stability of semigroups of operators |
| title_sort | weighted and local stability of semigroups of operators |
| work_keys_str_mv | AT battyc weightedandlocalstabilityofsemigroupsofoperators AT yeatess weightedandlocalstabilityofsemigroupsofoperators |