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A simple characterization of chaos for weighted composition $ C_0$-semigroups on Lebesgue and Sobolev spaces


Author: T. Kalmes
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
Published electronically: August 12, 2015
MathSciNet review: 3451233
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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.


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Additional Information

T. Kalmes
Affiliation: Fakultät für Mathematik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
Email: thomas.kalmes@mathematik.tu-chemnitz.de

DOI: https://doi.org/10.1090/proc/12794
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
Article copyright: © Copyright 2015 American Mathematical Society