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arXiv · 1707.03627

Dynamics and spectra of composition operators on the Schwartz space

Carmen Fernández·Antonio Galbis·Enrique Jordá
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Abstract

In this paper we study the dynamics of the composition operators defined in the Schwartz space $\mathcal{S}(\mathbb{R})$ of rapidly decreasing functions. We prove that such an operator is never supercyclic and, for monotonic symbols, it is power bounded only in trivial cases. For a polynomial symbol $φ$ of degree greater than one we show that the operator is mean ergodic if and only if it is power bounded and this is the case when $φ$ has even degree and lacks fixed points. We also discuss the spectrum of composition operators.

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Carmen Fernández, Antonio Galbis, Enrique Jordá. 2017-07-12. Dynamics and spectra of composition operators on the Schwartz space. https://arxiv.org/abs/1707.03627

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