On uniform exponential stability and exact admissibility of discrete semigroups
type: Item
instance of: scholarly article
title: On uniform exponential stability and exact admissibility of discrete semigroups
zbMATH Open document ID: 1328.39008
DOI: 10.1155/2013/268309
author: Aftab Khan
author: Gul Rahmat
author: Akbar Zada
published in: International Journal of Differential Equations
publication date: 2014-06-30T00:00:00Z
review text: The authors show that a discrete semigroup \((T(n))_{n\in\mathbb Z_+}\) of bounded linear operators acting on a complex Banach space \(X\) is uniformly exponentially stable if and only if for each \(x\in AP_0(\mathbb Z_+,X)\), the sequence \(n\to\sum_{k=0}^nT(n-k)x(k):\mathbb Z_+\to X\) belongs to \(AP_0(\mathbb Z_+,X)\).
reviewed by: Pham Viet Hai
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 39A70
zbMATH DE Number: 6309726
zbMATH Keywords: uniform exponential stability
zbMATH Keywords: exact admissibility
zbMATH Keywords: discrete semigroup
zbMATH Keywords: bounded linear operator
zbMATH Keywords: complex Banach space
Wikidata QID: Q58923585
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/268309
OpenAlex ID: W2100385836
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description: scientific article