Characterizations of stability for discrete semigroups of bounded linear operators
Journal: International Journal of Mathematics and Soft Computing (Vol.3, No. 3)Publication Date: 2013-07-10
Authors : Akbar Zada Gul Rahmat Afshan Tabassum Gohar Ali;
Page : 15-19
Keywords : Uniform stability; semigroups; periodic sequences;
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.
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Last modified: 2013-08-24 12:38:13