Individual Exponential Stability for Evolution Families of Linear and Bounded Operators

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

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
URI https://vuir.vu.edu.au/id/eprint/17256
Subjects Historical > FOR Classification > 0102 Applied Mathematics
Historical > FOR Classification > 0103 Numerical and Computational Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords spectral radius of bounded operator, normed function spaces, operator semigroup, q-periodic evolution family, growth bound, exponentially stable
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