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Journal of Operator Theory

Volume 80, Issue 1,  Summer  2018  pp. 213-224.

Multiplicative structures of hypercyclic functions for convolution operators

Authors:  Luis Bernal-Gonzalez (1), J. Alberto Conejero (2), George Costakis (3), and Juan B. Seoane-Sepulveda (4)
Author institution: (1) Departamento de Analisis Matematico, Facultad de Matematicas, Universidad de Sevilla, Avenida Reina Mercedes, 41080 Sevilla, Spain
(2) Instituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, 46022 Valencia, Spain
(3) Department of Mathematics and Applied Mathematics, University of Crete, Voutes Campus, 70013 Heraklion, Crete, Greece
(4) IMI and Departamento de Analisis Matematico, Facultad de Ciencias Matematicas, Plaza de Ciencias 3, Universidad Complutense de Madrid, 28040 Madrid, Spain

Summary:  In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function $1$, hypercyclic with respect to the convolution operator associated to a given entire function of subexponential type. A certain stability under multiplication is also shown for compositional hypercyclicity on complex domains.

Keywords:  Hypercyclic operator, convolution operator, composition operator, group of non-vanishing entire functions, subexponential growth, lineability, spaceability

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