Exponential dichotomy for evolution families on the real line
We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair (Lp(ℝ,X),Lq(ℝ,X)). We show that the admissibility of the pair (Lp(ℝ,X),Lq(ℝ,X)) is equivalent to the uniform exponential dichotomy of an evolution family if a...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/31641 |
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| _version_ | 1832564747085545472 |
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| author | Adina Luminiţa Sasu |
| author_facet | Adina Luminiţa Sasu |
| author_sort | Adina Luminiţa Sasu |
| collection | DOAJ |
| description | We give necessary and sufficient conditions for uniform
exponential dichotomy of evolution families in terms of the admissibility of the pair (Lp(ℝ,X),Lq(ℝ,X)). We show that the admissibility of the pair (Lp(ℝ,X),Lq(ℝ,X)) is equivalent to the uniform exponential dichotomy of an evolution family if and only if p≥q. As applications we obtain characterizations for uniform exponential dichotomy of semigroups. |
| format | Article |
| id | doaj-art-4bffc13766de4bc1a397a974f5be14d7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4bffc13766de4bc1a397a974f5be14d72025-02-03T01:10:17ZengWileyAbstract and Applied Analysis1085-33751687-04092006-01-01200610.1155/AAA/2006/3164131641Exponential dichotomy for evolution families on the real lineAdina Luminiţa Sasu0Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, Boulevard Vasile Pârvan No. 4, Timişoara 300223, RomaniaWe give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair (Lp(ℝ,X),Lq(ℝ,X)). We show that the admissibility of the pair (Lp(ℝ,X),Lq(ℝ,X)) is equivalent to the uniform exponential dichotomy of an evolution family if and only if p≥q. As applications we obtain characterizations for uniform exponential dichotomy of semigroups.http://dx.doi.org/10.1155/AAA/2006/31641 |
| spellingShingle | Adina Luminiţa Sasu Exponential dichotomy for evolution families on the real line Abstract and Applied Analysis |
| title | Exponential dichotomy for evolution families on the real line |
| title_full | Exponential dichotomy for evolution families on the real line |
| title_fullStr | Exponential dichotomy for evolution families on the real line |
| title_full_unstemmed | Exponential dichotomy for evolution families on the real line |
| title_short | Exponential dichotomy for evolution families on the real line |
| title_sort | exponential dichotomy for evolution families on the real line |
| url | http://dx.doi.org/10.1155/AAA/2006/31641 |
| work_keys_str_mv | AT adinaluminitasasu exponentialdichotomyforevolutionfamiliesontherealline |