Supercyclic Weighted Composition Operators on the Space of Smooth Functions

Juan Bès () and Christopher Foster
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Juan Bès: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA
Christopher Foster: Department of Mathematical Sciences, University of Cincinnati, 2815 Commons Way, Cincinnati, OH 45221, USA

Mathematics, 2025, vol. 13, issue 18, 1-19

Abstract: A weighted composition operator on the space of scalar-valued smooth functions on an open subset of a d-dimensional Euclidean space is supercyclic if and only if it is weakly mixing, and it is strongly supercyclic if and only if it is mixing. Every such mixing operator is chaotic. In the one-dimensional case, it is supercyclic if and only if it is mixing and if and only if it is chaotic.

Keywords: weighted composition operators; chaotic operators; hypercyclic operators; supercyclic operators; mixing operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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