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We investigate (uniform) mean ergodicity of (weighted) composition operators on the space of smooth functions and the space of distributions, respectively, both over an open subset of the real line. Among other things, we prove that a composition operator with a real analytic diffeomorphic symbol is mean ergodic on the space of distributions if and only if it is periodic (with period 2). Our results are based on a characterization of mean ergodicity in terms of Ces`aro boundedness and a growth property of the orbits for operators on Montel spaces which is of independent interest.
We study topologizability and power boundedness of weigh-ted composition operators on (certain subspaces of) $mathscr{D}(X)$ for an open subset $X$ of $mathbb{R}^d$. For the former property we derive a characterization in terms of the symbol and the
We characterize the (essentially) decreasing sequences of positive numbers $beta$ = ($beta$ n) for which all composition operators on H 2 ($beta$) are bounded, where H 2 ($beta$) is the space of analytic functions f in the unit disk such that $infty$
We provide explicit sequence space representations for the test function and distribution spaces occurring in the Valdivia-Vogt structure tables by making use of Wilson bases generated by compactly supported smooth windows. Furthermore, we show that
We study topological transitivity/hypercyclicity and topological (weak) mixing for weighted composition operators on locally convex spaces of scalar-valued functions which are defined by local properties. As main application of our general approach w
We give sufficient conditions for compactness of localization operators on modulation spaces $textbf{M}^{p,q}_{m_{lambda}}( mathbb{R}^{d})$ of $omega$-tempered distributions whose short-time Fourier transform is in the weighted mixed space $L^{p,q}_{m_lambda}$ for $m_lambda(x)=e^{lambdaomega(x)}$.