Rate of growth of hypercyclic and frequently hypercyclic functions for the Dunkl operator

2015/08/28 by Bernal-Gonzalez, Luis, Bonilla, Antonio
#30D15 #47A16 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1508.07180

Abstract

For the Dunkl operator Λ_α (α> -1/2) on the space of entire functions on the complex space C, the critical rate of growth for the integral means M_p(f,r) of their hypercyclic functions f is obtained. The rate of growth of the corresponding frequently hypercyclic functions is also analyzed.

Related

• Growth of entire functions: from frequent hypercyclicity to hypercyclicity for the differentiation operator
• Optimal growth of frequently hypercyclic entire functions
• Growth of (frequently) hypercyclic entire functions for differential operators
• Optimal growth of upper frequently hypercyclic functions for some weighted Taylor shifts
• Frequent hypercyclicity of random entire functions for the\n differentiation operator