On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups. (10th July 2013)

• Record Type: Journal Article
• Authors: Khan, Aftab; Rahmat, Gul; Zada, Akbar
• Other Names: Ntouyas Sotiris Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2013(2013)
• Publication Date: 2013-07-10
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2013/268309
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : We prove that a discrete semigroup𝕋 = { T ( n ) : n ∈ ℤ + } of bounded linear operators acting on a complex Banach spaceX is uniformly exponentially stable if and only if, for eachx ∈ A P 0 ( ℤ +, X ), the sequencen ↦ ∑ k = 0 n ‍ T ( n - k ) x ( k ) : ℤ + → X belongs toA P 0 ( ℤ +, X ) . Similar results for periodic discrete evolution families are also stated.