Spectrally determined growth is generic
HTML articles powered by AMS MathViewer
- by Michael Renardy
- Proc. Amer. Math. Soc. 124 (1996), 2451-2453
- DOI: https://doi.org/10.1090/S0002-9939-96-03417-X
- PDF | Request permission
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
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- Jan Prüss, On the spectrum of $C_{0}$-semigroups, Trans. Amer. Math. Soc. 284 (1984), no. 2, 847–857. MR 743749, DOI 10.1090/S0002-9947-1984-0743749-9
- Michael Renardy, On the linear stability of hyperbolic PDEs and viscoelastic flows, Z. Angew. Math. Phys. 45 (1994), no. 6, 854–865. MR 1306936, DOI 10.1007/BF00952081
- J. Zabczyk, A note on $C_{0}$-semigroups, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 23 (1975), no. 8, 895–898 (English, with Russian summary). MR 383144
Bibliographic Information
- Michael Renardy
- Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
- Email: renardym@math.vt.edu
- 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 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2451-2453
- MSC (1991): Primary 47D06
- DOI: https://doi.org/10.1090/S0002-9939-96-03417-X
- MathSciNet review: 1328372