Stability and dichotomy of positive semigroups on $L_p$
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- by Stephen Montgomery-Smith PDF
- Proc. Amer. Math. Soc. 124 (1996), 2433-2437 Request permission
Abstract:
A new proof of a result of Lutz Weis is given, that states that the stability of a positive strongly continuous semigroup $(e^{tA})_{t \ge 0}$ on $L_p$ may be determined by the quantity $s(A)$. We also give an example to show that the dichotomy of the semigroup may not always be determined by the spectrum $\sigma (A)$.References
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Additional Information
- Stephen Montgomery-Smith
- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- Email: stephen@math.missouri.edu
- Received by editor(s): June 14, 1994
- Received by editor(s) in revised form: February 17, 1995
- Additional Notes: Research supported in part by N.S.F. Grant D.M.S. 9201357.
- Communicated by: Dale Alspach
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2433-2437
- MSC (1991): Primary 47-02, 47D06; Secondary 35B40
- DOI: https://doi.org/10.1090/S0002-9939-96-03356-4
- MathSciNet review: 1327030