Hypercyclicity, existence and approximation results for convolution operators on spaces of entire functions

2018/05/25 by Vinícius V. Fávaro, Fávaro, Vinícius V., Ariosvaldo M. Jatobá +1
Mathematics · #46E10 #46E50 #46G20 #47A16 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46E10 #msc:46E50 #msc:46G20 #msc:47A16

paper · pdf · doi:10.48550/arxiv.1805.10316

25 pages

arxiv created 2018/05/25 · arxiv updated 2018/05/29

Abstract

In this work we shall prove new results on the theory of convolution operators on spaces of entire functions. The focus is on hypercyclicity results for convolution operators on spaces of entire functions of a given type and order; and existence and approximation results for convolution equations on spaces of entire functions of a given type and order. In both cases we give a general method to prove new results that recover, as particular cases, several results of the literature. Applications of these more general results are given, including new hypercyclicity results for convolution operators on spaces on entire functions on ℂⁿ.

Related

• Hypercyclicity of convolution operators on spaces of entire functions
• Strongly mixing convolution operators on Fréchet spaces of holomorphic functions
• Algebrable sets of hypercyclic vectors for convolution operators
• Chaos in convolution operators on the space of entire functions of infinitely many complex variables
• Multiplicative structures of hypercyclic functions for convolution operators