Integral characterizations for the dichotomy of evolution families
type: Item
instance of: scholarly article
title: Integral characterizations for the dichotomy of evolution families
zbMATH Open document ID: 1158.47026
author: Ciprian Preda
author: Petre Preda
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2008-08-11T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1210254819
review text: In this paper, some results by Datko, Pazy, Barbashin and others on the existence of uniform exponential dichotomies for evolution families \(\Phi\) on a Banach space \(X\) are generalized. Under the assumption that a dichotomy projector family exists, i.e., a strongly continuous projector-valued function \(P:[0,\infty)\to L(X)\) with \(\Phi(t,t_0)P(t_0)=P(t)\Phi(t,t_0)\) and the property that \(\Phi(t,t_0):\mathrm{Ker}\,(P(t_0))\to\mathrm{Ker}\,(P(t))\) is an isomorphism, the authors give necessary and sufficient integral conditions under which the evolution family possesses a uniform exponential dichotomy with projections \(P\).
reviewed by: Jörg Härterich
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 37L05
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34D09
zbMATH DE Number: 5309607
zbMATH Keywords: uniform exponential dichotomy
zbMATH Keywords: evolution family
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5309607