A Theorem of Rolewicz's Type for Measurable Evolution Families in Banach Spaces
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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 satisfying 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. Electronic Journal of Differential Equations, 2001(70), pp. 1-5.
Rights
Attribution 4.0 International