# Journal of Operator Theory

Volume 77, Issue 1, Winter 2017  pp. 39-59.

Hypercyclic behavior of some non-convolution operators on $H(\mathbf{C}^N)$

Authors:  Santiago Muro (1), Damian Pinasco (2), and Martin Savransky (3)
Author institution:(1) Departamento de Matematica - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428), Ciudad Autonoma de Buenos Aires, Argentina and CONICET
(2) Departamento de Matematicas y Estadistica, Universidad Torcuato Di Tella, Av. Figueroa Alcorta 7350, (1428), Ciudad Autonoma de Buenos Aires, Argentina and CONICET
(3) Departamento de Matematica - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428), Ciudad Autonoma de Buenos Aires, Argentina and CONICET

Summary: We study hypercyclicity properties of a family of non-convolution operators defined on the spaces of entire functions on $\mathbb{C}^N$. These operators are a composition of a differentiation operator and an affine composition operator, and are analogues of operators studied by Aron and Markose on $H(\mathbb{C})$. The hypercyclic behavior is more involved than in the one dimensional case, and depends on several parameters involved.

DOI: http://dx.doi.org/10.7900/jot.2015oct08.2127
Keywords: non-convolution operators, differentiation operators, composition operators, frequently hypercyclic operators, strongly mixing operators