Characteristic conditions for a $c_ 0$-semigroup with continuity in the uniform operator topology for $t>0$ in Hilbert space
HTML articles powered by AMS MathViewer
- by Pu Hong You PDF
- Proc. Amer. Math. Soc. 116 (1992), 991-997 Request permission
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
- A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486, DOI 10.1007/978-1-4612-5561-1
- Fa Lun Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces, Ann. Differential Equations 1 (1985), no. 1, 43–56. MR 834231
Additional Information
- © Copyright 1992 American Mathematical Society
- 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