A simple characterization of chaos for weighted composition 𝐶₀-semigroups on Lebesgue and Sobolev spaces

Kalmes, T.

doi:10.1090/proc/12794

A simple characterization of chaos for weighted composition $C_0$-semigroups on Lebesgue and Sobolev spaces
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Proc. Amer. Math. Soc. 144 (2016), 1561-1573 Request permission

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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