Common hypercyclic functions for translation operators with large gaps\n II

2014/12/05 by Nikos Tsirivas, Tsirivas, Nikos
Mathematics · #47A16 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1412.1963

openalex publication_date 2014/12/05 · openalex created_date 2016/12/16 · openalex updated_date 2026/07/28

Abstract

We prove the existence of common hypercyclic entire functions for uncountable\nfamilies of translation type operators. Contrary to our previous work [34],\nhere the parameter which reflects the uncountable family lies on the unit\ncircle. On the other hand the sequence of translations is in a sense less\nrestrictive if it is to be compared with the corresponding sequence in [34].\nOur result largely extends a result of Costakis in [19].\n

Citations

• Common hypercyclic vectors for composition operators
• Non-existence of common hypercyclic entire functions for certain\n families of translation operators

Related

• Common hypercyclic functions for translation operators with large gaps
• Non-existence of common hypercyclic entire functions for certain\n families of translation operators
• Existence of common hypercyclic vectors for translation operators
• Existence of common hypercyclic subspaces for the derivative operator\n and the translation operators
• Common hypercyclic vectors and universal functions