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Journal of Operator Theory

Volume 46, Issue 1, Summer 2001  pp. 63-98.

A resolvent approach to stability of operator semigroups

Authors:  Yuri Tomilov
Author institution: Department of Dynamical Systems, Institute of Mathematics, Tereshchenkivska Str.~3, 252601 Kiev-4, Ukraine

Summary:  It is proposed to characterize stability of strongly continuous and discrete operator semigroups in Banach and Hilbert spaces in terms of local resolvents of their ``generators". Several such criterias are given and their relations to the previous results are discussed.

Keywords:  Operator semigroups, stability, resolvent

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