Perron conditions for exponential expansiveness of one-parameter semigroup
We present a new approach for the theorems of Perron type for exponential expansiveness of one-parameter semigroups in terms of<em> l^p(N, X)</em> spaces. We prove that an exponentially bounded semigroup is exponentially expansive if and only if the pair <em>(l^p (N, X), l^q(N, X))...
| 發表在: | Le Matematiche |
|---|---|
| 主要作者: | |
| 格式: | Article |
| 語言: | 英语 |
| 出版: |
Università degli Studi di Catania
2003-05-01
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| 在線閱讀: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/183 |
| _version_ | 1852803338194649088 |
|---|---|
| author | Bogdan Sasu |
| author_facet | Bogdan Sasu |
| author_sort | Bogdan Sasu |
| collection | DOAJ |
| container_title | Le Matematiche |
| description | We present a new approach for the theorems of Perron type for exponential expansiveness of one-parameter semigroups in terms of<em> l^p(N, X)</em> spaces. We prove that an exponentially bounded semigroup is exponentially expansive if and only if the pair <em>(l^p (N, X), l^q(N, X))</em> is completely admissible relative to a discrete equation associated to the semigroup, where<em> p, q ∈ [1, ∞), p ≥ q</em>. We apply our results in order to obtain very general characterizations for exponential expansiveness of <em>C_0</em>-semigroups in terms of the complete admissibility of the pair <em>(L^ p (R_+ , X), L^ q (R_+ , X)) </em>and for exponential dichotomy, respectively, in terms of the admissibility of the pair <em>(L^p(R_+,X),</em> <em>L^q(R_+,X))</em>.<br /> |
| format | Article |
| id | doaj-art-e94e9c233a3e4b79abd0c4467db5394e |
| institution | Directory of Open Access Journals |
| issn | 0373-3505 2037-5298 |
| language | English |
| publishDate | 2003-05-01 |
| publisher | Università degli Studi di Catania |
| record_format | Article |
| spelling | doaj-art-e94e9c233a3e4b79abd0c4467db5394e2025-08-19T20:39:04ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52982003-05-01581101115161Perron conditions for exponential expansiveness of one-parameter semigroupBogdan SasuWe present a new approach for the theorems of Perron type for exponential expansiveness of one-parameter semigroups in terms of<em> l^p(N, X)</em> spaces. We prove that an exponentially bounded semigroup is exponentially expansive if and only if the pair <em>(l^p (N, X), l^q(N, X))</em> is completely admissible relative to a discrete equation associated to the semigroup, where<em> p, q ∈ [1, ∞), p ≥ q</em>. We apply our results in order to obtain very general characterizations for exponential expansiveness of <em>C_0</em>-semigroups in terms of the complete admissibility of the pair <em>(L^ p (R_+ , X), L^ q (R_+ , X)) </em>and for exponential dichotomy, respectively, in terms of the admissibility of the pair <em>(L^p(R_+,X),</em> <em>L^q(R_+,X))</em>.<br />http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/183 |
| spellingShingle | Bogdan Sasu Perron conditions for exponential expansiveness of one-parameter semigroup |
| title | Perron conditions for exponential expansiveness of one-parameter semigroup |
| title_full | Perron conditions for exponential expansiveness of one-parameter semigroup |
| title_fullStr | Perron conditions for exponential expansiveness of one-parameter semigroup |
| title_full_unstemmed | Perron conditions for exponential expansiveness of one-parameter semigroup |
| title_short | Perron conditions for exponential expansiveness of one-parameter semigroup |
| title_sort | perron conditions for exponential expansiveness of one parameter semigroup |
| url | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/183 |
| work_keys_str_mv | AT bogdansasu perronconditionsforexponentialexpansivenessofoneparametersemigroup |