STRONGLY MIXING CONVOLUTION OPERATORS IN THE GAUSSIAN SENSE

SAVRANSKY MARTIN

MADRID

Congreso; FUNCTION THEORY ON INFINITE DIMENSIONAL ANALYSIS XIII; 2014

UNIVERSIDAD AUTONOMA DE MADRID

A theorem of Godefroy and Shapiro [3] states that non-trivial con- volution operators on H(C n ) are hypercyclic. This theorem was improved in [2], where it is shown that non-trivial convolution operators are frequently hypercyclic and that there are frequently hypercyclic entire functions of exponential growth. Using new technics developed independently by Bayart and Matheron [1] and by Murillo-Arcila and Peris [4], we prove that non-trivial convolution operators de- fined on the space of entire functions of bounded type associated to a holomorphy type are strongly mixing with respect to a gaussian probability measure. Also we prove the existence of frequently hypercyclic entire functions of exponential growth.