## 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).

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## 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 |
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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 |

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