A Characterization of Strongly Continuous Groups of Linear Operators on a Hilbert Space |
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Authors: | Liu Kangsheng |
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Institution: | Department of Applied Mathematics, Zhejiang University Hangzhou, 310027, China |
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Abstract: | It is proved that the infinitesimal generator A of a stronglycontinuous semigroup of linear operators on a Hilbert spacealso generates a strongly continuous group if and only if theresolvent of A, ( + A)1, is also a bounded functionon some right-hand-side half plane of complex numbers, and convergesstrongly to zero as the real part of tends to infinity. Anapplication to a partial differential equation is given. 1991Mathematics Subject Classification 47D03. |
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