Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the Rolewicz theorem for evolution operators


Author: K. V. Storozhuk
Journal: Proc. Amer. Math. Soc. 135 (2007), 1861-1863
MSC (2000): Primary 47D06; Secondary 34G10
DOI: https://doi.org/10.1090/S0002-9939-07-08697-2
Published electronically: January 5, 2007
MathSciNet review: 2286097
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a short proof of a generalization of the Rolewicz theorem based on the uniform boundedness principle.


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

  • [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)
  • [2] R. Datko, Extending a theorem of A. M. Liapounov to Hilbert space, J. Math. Anal. Appl. 32 (1970), 610 - 616.MR 0268717 (42:3614)
  • [3] 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)
  • [5] J. M. A. M. van Neerven, On the orbits of an operator with spectral radius one, Czechoslovak Math. J. 45(120) (1995), 3, 495-502.MR 1344516 (96f:47009)
  • [6] J. M. A. M. van Neerven, M. Lower semicontinuity and the theorem of Datko and Pazy, Integral Equations Operator Theory 42 (2002), 4, 482-492.MR 1885446 (2003i:47044)
  • [7] S. Rolewicz, On uniform $ N$-equistability, J. Math. Anal. Appl. 115 (1986), 434-441.MR 0836237 (87h:47100)
  • [8] 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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47D06, 34G10

Retrieve articles in all journals with MSC (2000): 47D06, 34G10


Additional Information

K. V. Storozhuk
Affiliation: Sobolev Institute of Mathematics, Acad. Koptyug pr. 4, 630090 Novosibirsk, Russia

DOI: https://doi.org/10.1090/S0002-9939-07-08697-2
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
Published electronically: 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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society