English

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}
}

Comments

17 pages

R2 v1 2026-07-01T04:13:06.479Z