Generalized Exponential Trichotomies for Abstract Evolution Operators on the Real Line
This paper considers two trichotomy concepts in the context of abstract evolution operators. The first one extends the notion of exponential trichotomy in the sense of Elaydi-Hajek for differential equations to abstract evolution operators, and it is a natural extension of the generalized exponentia...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/409049 |
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| _version_ | 1832553990020136960 |
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| author | Nicolae Lupa Mihail Megan |
| author_facet | Nicolae Lupa Mihail Megan |
| author_sort | Nicolae Lupa |
| collection | DOAJ |
| description | This paper considers two trichotomy concepts in the context of abstract evolution operators. The first one extends the notion of exponential trichotomy in the sense of Elaydi-Hajek for differential equations to abstract evolution operators, and it is a natural extension of the generalized exponential dichotomy considered in the paper by Jiang (2006). The second concept is dual in a certain sense to the first one. We prove that these types of exponential trichotomy imply the existence of generalized exponential dichotomy on both half-lines. We emphasize that we do not assume the invertibility of the evolution operators on the whole space X (unlike the case of evolution operators generated
by differential equations). |
| format | Article |
| id | doaj-art-0040fabafeea4f4e914dd44a371393a5 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-0040fabafeea4f4e914dd44a371393a52025-02-03T05:52:32ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/409049409049Generalized Exponential Trichotomies for Abstract Evolution Operators on the Real LineNicolae Lupa0Mihail Megan1Faculty of Economics and Business Administration, West University of Timişoara, Boulevard Pestalozzi 16, 300115 Timişoara, RomaniaAcademy of Romanian Scientists, Independenţei 54, 050094 Bucharest, RomaniaThis paper considers two trichotomy concepts in the context of abstract evolution operators. The first one extends the notion of exponential trichotomy in the sense of Elaydi-Hajek for differential equations to abstract evolution operators, and it is a natural extension of the generalized exponential dichotomy considered in the paper by Jiang (2006). The second concept is dual in a certain sense to the first one. We prove that these types of exponential trichotomy imply the existence of generalized exponential dichotomy on both half-lines. We emphasize that we do not assume the invertibility of the evolution operators on the whole space X (unlike the case of evolution operators generated by differential equations).http://dx.doi.org/10.1155/2013/409049 |
| spellingShingle | Nicolae Lupa Mihail Megan Generalized Exponential Trichotomies for Abstract Evolution Operators on the Real Line Journal of Function Spaces and Applications |
| title | Generalized Exponential Trichotomies for Abstract Evolution
Operators on the Real Line |
| title_full | Generalized Exponential Trichotomies for Abstract Evolution
Operators on the Real Line |
| title_fullStr | Generalized Exponential Trichotomies for Abstract Evolution
Operators on the Real Line |
| title_full_unstemmed | Generalized Exponential Trichotomies for Abstract Evolution
Operators on the Real Line |
| title_short | Generalized Exponential Trichotomies for Abstract Evolution
Operators on the Real Line |
| title_sort | generalized exponential trichotomies for abstract evolution operators on the real line |
| url | http://dx.doi.org/10.1155/2013/409049 |
| work_keys_str_mv | AT nicolaelupa generalizedexponentialtrichotomiesforabstractevolutionoperatorsontherealline AT mihailmegan generalizedexponentialtrichotomiesforabstractevolutionoperatorsontherealline |