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Characterizations of stability for discrete semigroups of bounded linear operators

Journal: International Journal of Mathematics and Soft Computing (Vol.3, No. 3)

Publication Date:

Authors : ;

Page : 15-19

Keywords : Uniform stability; semigroups; periodic sequences;

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Abstract

Let $mathbb{T}={T(n)}_{ngeq 0}$ be a discrete semigroup of bounded linear operators acting on a Banach space $X$. We prove that if for each $mu in mathbb{R}$ and every $q$-periodic sequence $f$ with $f(0)=0$, the sequence $nrightarrow sum_{k=0}^{n}e^{imu k}T(n-k)f(k)$ is bounded, then the semigroup $mathbb{T}$ is uniformly exponentially stable.

Last modified: 2013-08-24 12:38:13