A SHARP RESULT ON THE EXPONENTIAL OPERATOR-NORM DECAY OF A FAMILY OF STRONGLY CONTINUOUS SEMIGROUPS

被引：11

作者：

TRIGGIANI, R ^{[1
]}

机构：

[1] UNIV VIRGINIA,DEPT APPL MATH,CHARLOTTESVILLE,VA 22903

来源：

SEMIGROUP FORUM | 1994年 / 49卷 / 03期

关键词：

D O I：

10.1007/BF02573499

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a family T(h)(t) of strongly continuous semigroups on a Banach space X, we give a sharp result on the exponential decay in L(X) of the family, which is uniform in the parameter h. Sharpness is shown by means of counterexamples. This result generalizes a well-known and very useful criterion of stability of a single strongly continuous semigroup. The obtained generalization plays a critical role in a variety of applications, from approximation theory to regularization theory.

引用

页码：387 / 395

页数：9