A simple characterization of chaos for weighted composition $C_0$-semigroups on Lebesgue and Sobolev spaces
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Abstract:
We give a simple characterization of chaos for weighted composition $C_0$-semigroups on $L^p_\rho (\Omega )$ for an open interval $\Omega \subseteq \mathbb {R}$. Moreover, we characterize chaos for these classes of $C_0$-semigroups on the closed subspace $W^{1,p}_*(\Omega )$ of the Sobolev space $W^{1,p}(\Omega )$ for a bounded interval $\Omega \subset \mathbb {R}$. These characterizations simplify the characterization of chaos obtained by Aroza, Kalmes, and Mangino (2014) for these classes of $C_0$-semigroups.References
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Additional Information
- T. Kalmes
- Affiliation: Fakultät für Mathematik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
- MR Author ID: 717771
- Email: thomas.kalmes@mathematik.tu-chemnitz.de
- Received by editor(s): September 15, 2014
- Received by editor(s) in revised form: April 2, 2015
- Published electronically: August 12, 2015
- Communicated by: Yingfei Yi
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1561-1573
- MSC (2010): Primary 47A16, 47D06; Secondary 35F15, 35F10
- DOI: https://doi.org/10.1090/proc/12794
- MathSciNet review: 3451233