Asymptotic behavior of discrete and continuous semigroups on Hilbert spaces

被引:0
|
作者
Buse, Constantin [1 ]
Prajea, Manuela-Suzy [2 ]
机构
[1] West Univ Timisoara, Dept Math, Timisoara 300223, Romania
[2] Natl Coll Traian, Drobeta Turnu Severin, Romania
关键词
spectral radius; discrete semigroups; strongly continuous semigroups; uniform exponential stability; Orlicz space;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let phi : [0, infinity) -> [0, infinity) be a nondecreasing function with phi(t) > 0 for all t > 0, H be a complex Hilbert space and let T be a bounded linear operator acting on H. Among our results is the fact that T is power stable (i.e. its spectral radius is less than 1) if [GRAPHICS] for all x E H with parallel to x parallel to <= 1. In the continuous case we prove that a strongly continuous uniformly bounded semigroup of operators acting on a Hilbert space H is spectrally stable (i.e. the spectrum of its infinitesimal generator lies in the open left half plane) if and only if for each x is an element of H and each mu is an element of R one has: [GRAPHICS]
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页码:123 / 135
页数:13
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