MULTIPLICATIVE PERTURBATIONS OF C-0-SEMIGROUPS AND SOME APPLICATIONS TO STEP RESPONSES AND CUMULATIVE OUTPUTS

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/28027

Title:	MULTIPLICATIVE PERTURBATIONS OF C-0-SEMIGROUPS AND SOME APPLICATIONS TO STEP RESPONSES AND CUMULATIVE OUTPUTS
Authors:	PISKAREV,S;SHAW,SY
Contributors:	數學研究所
Date:	1995
Issue Date:	2010-06-29 19:40:32 (UTC+8)
Publisher:	中央大學
Abstract:	For a C-o-semigroup T(.), we prove a general multiplicative perturbation theorem which subsumes many known multiplicative and additive perturbation theorems, and provides a general framework for systematic study of the perturbation associated with a step response U(.) of a linear dynamical system. If the semivariation SV(U(.), t) of U(.) on [0, t] tends to 0 as t-->0(+), then the infinitesimal operator A(s) of the pair (T(.), U(.)), as a mixed-type perturbation of the generator A of T(.), generates a C-o-semigroup T-s(.) with parallel to T-s(t)-T(t)parallel to=0(1)(t-->0(+)). Furthermore, C-o-semigroups S(.) which satisfy parallel to S(t)-T(t)parallel to=O(t)(t-->0(+)) are exactly those mixed-type perturbations caused by Lipschitz continuous step responses. Perturbations related to a cumulative output V(.) are also investigated by using a multiplicative perturbation theorem of Desch and Schappacher. In particular, we show that bounded additive perturbations of A are exactly those mixed-type perturbations caused by Lipschitz continuous cummulative outputs. It is also shown that the generator of T(.) is bounded if and only if SV(T(.), t) is sufficiently small for all small t. (C) 1995 Academic Press, Inc.
Relation:	JOURNAL OF FUNCTIONAL ANALYSIS
Appears in Collections:	[Graduate Institute of Mathematics] journal & Dissertation

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