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.
DOI: http://dx.doi.org/10.7900/jot.2017sep27.2162
Keywords: Hypercyclic operator, convolution operator, composition operator,
group of non-vanishing entire functions, subexponential growth, lineability, spaceability
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