Growth of entire functions: from frequent hypercyclicity to hypercyclicity for the differentiation operator

2025/06/15 by Augustin Mouze, Mouze, Augustin
Mathematics · #30D15 #30E25 #47A16 #47B37 #47B38 #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2506.12763

openalex publication_date 2025/06/15 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

We study the rate of growth of entire functions that are frequently hypercyclic with respect to some upper weighted densities for the differentiation operator. The statements obtained show the link between the minimal growth of frequently hypercyclic entire functions and that of hypercyclic entire functions. The results are optimal.

Citations

• Optimal growth of frequently hypercyclic entire functions

Related

• Optimal growth of frequently hypercyclic entire functions
• Rate of growth of hypercyclic and frequently hypercyclic functions for the Dunkl operator
• Growth of (frequently) hypercyclic entire functions for differential operators
• Frequent hypercyclicity of random entire functions for the\n differentiation operator
• Optimal growth of upper frequently hypercyclic functions for some weighted Taylor shifts