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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2013/268309 |