Supercyclic weighted composition operators on the space of smooth functions
Functional Analysis
2025-07-23 v1
Abstract
A weighted composition operator on the space of scalar-valued smooth functions on an open set of 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 mixing such 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
Cite
@article{arxiv.2507.16425,
title = {Supercyclic weighted composition operators on the space of smooth functions},
author = {J. Bes and C. Foster},
journal= {arXiv preprint arXiv:2507.16425},
year = {2025}
}
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17 pages