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

Key Points

• The study finds optimal relationships between growth rates of entire functions and hypercyclicity.
• It shows that minimal growth of frequently hypercyclic functions links to hypercyclic entire functions.
• The analysis explores upper weighted densities concerning the differentiation operator's growth behavior.
• Findings may influence understanding of function theory and operator behaviors within complex analysis.

Abstract