Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Spectrally determined growth is generic

Author(s): Michael Renardy
Journal: Proc. Amer. Math. Soc. 124 (1996), 2451-2453.
MSC (1991): Primary 47D06
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Let $A$ be the infinitesimal generator of a $C_0$-semigroup of operators in a Hilbert space. We consider the class of operators $A+B$, where $B$ is bounded. It is proved that the spectrum of $A+B$ determines the growth of the associated semigroup for ``most" operators $B$ (in the sense of Baire category).

References:

[1]
E. Hille and R. S. Phillips, Functional analysis and semigroups, American Mathematical Society, Providence, 1957. MR 19:664

[2]
J. Prüß, On the spectrum of $C_0$-semigroups, Trans. Amer. Math. Soc. 284 (1984), 847--857. MR 85f:47044

[3]
M. Renardy, On the linear stability of hyperbolic PDEs and viscoelastic flows, Z. Angew. Math. Phys. 45 (1994), 854--865. MR 95i:35195

[4]
J. Zabczyk, A note on $C_0$-semigroups, Bull. Acad. Polon. Sci., Ser. Sci. Math. 23 (1975), 895--898. MR 52:4025

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47D06

Retrieve articles in all Journals with MSC (1991): 47D06

Additional Information:

Michael Renardy
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
Email: renardym@math.vt.edu

DOI: 10.1090/S0002-9939-96-03417-X
PII: S 0002-9939(96)03417-X
Keywords: Linear stability, semigroups of operators
Received by editor(s): January 9, 1995
Received by editor(s) in revised form: February 23, 1995
Additional Notes: This research was supported by the National Science Foundation under Grant DMS--9306635 and by the Office of Naval Research under Grant N00014--92--J--1664.
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1996, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google