Pairs of Function Spaces and Exponential Dichotomy on the Real Line
We provide a complete diagram of the relation between the admissibility of pairs of Banach function spaces and the exponential dichotomy of evolution families on the real line. We prove that if W∈ℋ(ℝ) and V∈𝒯(ℝ) are two Banach funct...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/347670 |
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doaj-f03dda308de74aacab2550e686f37dc72020-11-25T00:09:24ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472010-01-01201010.1155/2010/347670Pairs of Function Spaces and Exponential Dichotomy on the Real LineAdina Luminiţa SasuWe provide a complete diagram of the relation between the admissibility of pairs of Banach function spaces and the exponential dichotomy of evolution families on the real line. We prove that if W∈ℋ(ℝ) and V∈𝒯(ℝ) are two Banach function spaces with the property that either W∈𝒲(ℝ) or V∈𝒱(ℝ), then the admissibility of the pair (W(ℝ,X),V(ℝ,X)) implies the existence of the exponential dichotomy. We study when the converse implication holds and show that the hypotheses on the underlying function spaces cannot be dropped and that the obtained results are the most general in this topic. Finally, our results are applied to the study of exponential dichotomy of C0-semigroups. http://dx.doi.org/10.1155/2010/347670 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Adina Luminiţa Sasu |
| spellingShingle |
Adina Luminiţa Sasu Pairs of Function Spaces and Exponential Dichotomy on the Real Line Advances in Difference Equations |
| author_facet |
Adina Luminiţa Sasu |
| author_sort |
Adina Luminiţa Sasu |
| title |
Pairs of Function Spaces and Exponential Dichotomy on the Real Line |
| title_short |
Pairs of Function Spaces and Exponential Dichotomy on the Real Line |
| title_full |
Pairs of Function Spaces and Exponential Dichotomy on the Real Line |
| title_fullStr |
Pairs of Function Spaces and Exponential Dichotomy on the Real Line |
| title_full_unstemmed |
Pairs of Function Spaces and Exponential Dichotomy on the Real Line |
| title_sort |
pairs of function spaces and exponential dichotomy on the real line |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1839 1687-1847 |
| publishDate |
2010-01-01 |
| description |
We provide a complete diagram of the relation between the admissibility of pairs of Banach function spaces and the exponential dichotomy of evolution families on the real line. We prove that if W∈ℋ(ℝ) and V∈𝒯(ℝ) are two Banach function spaces with the property that either W∈𝒲(ℝ) or V∈𝒱(ℝ), then the admissibility of the pair (W(ℝ,X),V(ℝ,X)) implies the existence of the exponential dichotomy. We study when the converse implication holds and show that the hypotheses on the underlying function spaces cannot be dropped and that the obtained results are the most general in this topic. Finally, our results are applied to the study of exponential dichotomy of C0-semigroups. |
| url |
http://dx.doi.org/10.1155/2010/347670 |
| work_keys_str_mv |
AT adinaluminiamp355asasu pairsoffunctionspacesandexponentialdichotomyontherealline |
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1725411988548354048 |