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On the Rolewicz theorem for evolution operators
Author(s):
K.
V.
Storozhuk
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1861-1863.
MSC (2000):
Primary 47D06;
Secondary 34G10
Posted:
January 5, 2007
MathSciNet review:
2286097
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Abstract:
We give a short proof of a generalization of the Rolewicz theorem based on the uniform boundedness principle.
References:
-
- [1]
- C. Buse, S. Dragomir, New characterizations of asymptotic stability for evolution families on Banach spaces, Electron. J. Differential Equations 2004, 38, 9 pp. (electronic). MR 2047394 (2005b:34112)
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- R. Datko, Extending a theorem of A. M. Liapounov to Hilbert space, J. Math. Anal. Appl. 32 (1970), 610 - 616.MR 0268717 (42:3614)
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- W. Littman, A generalization of a theorem of Datko and Pazy, in Lecture Notes in Control and Inform. Sci., v. 130, Springer-Verlag, Berlin, 1989, pp. 318-323.MR 1029070 (91a:47052)
- [4]
- A. Pazy, On the applicability of Lyapunov's theorem in Hilbert Space, SIAM J. Math. Anal., v.3 2 (1972), 291-294.MR 0317105 (47:5653)
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- Q. Zheng, Exponential stability and perturbation problems for linear evolution systems in Banach spaces (Chinese, English Review), J. Sichuan Univ. 25 (1988), 4, 401-411.MR 0995048 (90e:34110)
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Additional Information:
K.
V.
Storozhuk
Affiliation:
Sobolev Institute of Mathematics, Acad. Koptyug pr. 4, 630090 Novosibirsk, Russia
DOI:
10.1090/S0002-9939-07-08697-2
PII:
S 0002-9939(07)08697-2
Keywords:
$C_0$-semigroup,
evolution operator,
uniform exponential stability
Received by editor(s):
December 16, 2005
Received by editor(s) in revised form:
February 14, 2006
Posted:
January 5, 2007
Additional Notes:
The author was supported by the Program of Russian Federation, Grant NSh-8526.2006.1
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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