Supercyclic weighted composition operators on the space of smooth functions

2025/07/22 by Juan Bès, C. Foster, Bes, J. +1
Mathematics · #47A16 #47B33 #47B38 #Advanced Topics in Algebra #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2507.16425

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Dynamics of composition operators on spaces of holomorphic functions on plane domains
• Dynamics of composition operators on function spaces defined by local and global properties

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