Research Repository

Individual Exponential Stability for Evolution Families of Linear and Bounded Operators

Buse, Constantin and Pogan, Alin (1999) Individual Exponential Stability for Evolution Families of Linear and Bounded Operators. RGMIA research report collection, 2 (6).

[img] Text
nzjm.pdf
Restricted to Repository staff only

Download (176kB)

Abstract

Let R+ be the set of all non-negative real numbers, I ∈ {R,R+} and U = {U(t,s) : t ≥ s ∈ I} be a strongly continuous and exponentially bounded evolution family of bounded linear operators acting on a Banach space X. Let E be a normed function space over I satisfying some properties, see section 2. We prove that if �XI(•)||U(•,s)x|| defines an element of the space E for some s ∈ I and some x ∈ X, then there exists N(s, x) > 0 such that *mathematical equation Some related results for periodic evolution families are also proved.

Item Type: Article
Uncontrolled Keywords: spectral radius of bounded operator, normed function spaces, operator semigroup, q-periodic evolution family, growth bound, exponentially stable
Subjects: FOR Classification > 0102 Applied Mathematics
FOR Classification > 0103 Numerical and Computational Mathematics
Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Depositing User: Research Group in Mathematical Inequalities and Applications
Date Deposited: 19 Jul 2012 00:45
Last Modified: 23 May 2013 16:49
URI: http://vuir.vu.edu.au/id/eprint/17256
ePrint Statistics: View download statistics for this item

Repository staff only

View Item View Item

Search Google Scholar