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Characteristic conditions for a $ c\sb 0$-semigroup with continuity in the uniform operator topology for $ t>0$ in Hilbert space


Author: Pu Hong You
Journal: Proc. Amer. Math. Soc. 116 (1992), 991-997
MSC: Primary 47D03
DOI: https://doi.org/10.1090/S0002-9939-1992-1098405-7
MathSciNet review: 1098405
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Abstract: In this paper, we obtain necessary and sufficient conditions for a $ {c_0}$-semigroup with continuity in the uniform operator topology for $ t > 0$ in Hilbert space in terms of the spectral property of its infinitesimal generator. Then we get the characteristic theorem for the compact semigroup.


References [Enhancements On Off] (What's this?)

  • [1] A. Pazy, Semigroup of linear operators and application to partial differential equations, Springer-Verlag, New York, Berlin, Heidelberg, and Tokyo, 1983. MR 710486 (85g:47061)
  • [2] F. L. Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert space, Ann. Differential Equations 1 (1985), 43-56. MR 834231 (87e:34106)

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DOI: https://doi.org/10.1090/S0002-9939-1992-1098405-7
Article copyright: © Copyright 1992 American Mathematical Society

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