A Theorem of Rolewicz's Type for Measurable Evolution Families in Banach Spaces

Date

2001-11-23

Authors

Buse, Constantin
Dragomir, Sever S.

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

Let φ be a positive and non-decreasing function defined on the real half-line and U be a strongly measurable, exponentially bounded evolution family of bounded linear operators acting on a Banach space and satisfing a certain measurability condition as in Theorem 1 below. We prove that if φ and U satisfy a certain integral condition (see the relation 1 from Theorem 1 below) then U is uniformly exponentially stable. For φ continuous and U strongly continuous and exponentially bounded, this result is due to Rolewicz. The proofs uses the relatively recent techniques involving evolution semigroup theory.

Description

Keywords

Evolution family of bounded linear operators, Evolution operator semigroup, Rolewicz's theorem, Exponential stability

Citation

Buse, C., & Dragomir, S. S. (2001). A theorem of Rolewicz's type for measurable evolution families in Banach spaces. <i>Electronic Journal of Differential Equations, 2001</i>(70), pp. 1-5.

Rights

Attribution 4.0 International

Rights Holder

Rights License