On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups
We prove that a discrete semigroup 𝕋={T(n):n∈ℤ+} of bounded linear operators acting on a complex Banach space X is uniformly exponentially stable if and only if, for each x∈AP0(ℤ+,X), the sequence n↦∑k=0nT(n-k)x(k):ℤ+→X belongs to AP0(ℤ+,X). Similar results for periodic discrete evolution families...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2013/268309 |
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| _version_ | 1850225174388932608 |
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| author | Aftab Khan Gul Rahmat Akbar Zada |
| author_facet | Aftab Khan Gul Rahmat Akbar Zada |
| author_sort | Aftab Khan |
| collection | DOAJ |
| description | We prove that a discrete semigroup 𝕋={T(n):n∈ℤ+} of bounded linear operators acting on a complex Banach space X is uniformly exponentially stable if and only if, for each x∈AP0(ℤ+,X), the sequence n↦∑k=0nT(n-k)x(k):ℤ+→X belongs to AP0(ℤ+,X). Similar results for periodic discrete evolution families are also stated. |
| format | Article |
| id | doaj-art-5ad0a0d2eaea41ab9cb603b692f789ef |
| institution | OA Journals |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-5ad0a0d2eaea41ab9cb603b692f789ef2025-08-20T02:05:27ZengWileyInternational Journal of Differential Equations1687-96431687-96512013-01-01201310.1155/2013/268309268309On Uniform Exponential Stability and Exact Admissibility of Discrete SemigroupsAftab Khan0Gul Rahmat1Akbar Zada2Shaheed Benazir Bhutto University Sheringal, Dir Upper 18000, PakistanGovernment College University, Abdus Salam School of Mathematical Sciences (ASSMS), Lahore 54600, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanWe prove that a discrete semigroup 𝕋={T(n):n∈ℤ+} of bounded linear operators acting on a complex Banach space X is uniformly exponentially stable if and only if, for each x∈AP0(ℤ+,X), the sequence n↦∑k=0nT(n-k)x(k):ℤ+→X belongs to AP0(ℤ+,X). Similar results for periodic discrete evolution families are also stated.http://dx.doi.org/10.1155/2013/268309 |
| spellingShingle | Aftab Khan Gul Rahmat Akbar Zada On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups International Journal of Differential Equations |
| title | On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups |
| title_full | On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups |
| title_fullStr | On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups |
| title_full_unstemmed | On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups |
| title_short | On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups |
| title_sort | on uniform exponential stability and exact admissibility of discrete semigroups |
| url | http://dx.doi.org/10.1155/2013/268309 |
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