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))...
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
2003-05-01
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| Series: | Le Matematiche |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/183 |
| Summary: | 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 /> |
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| ISSN: | 0373-3505 2037-5298 |