INVESTIGADORES
MURO Luis Santiago Miguel
artículos
Título:
Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
Autor/es:
MURO, SANTIAGO; PINASCO, DAMIÁN; SAVRANSKY, MARTÍN
Revista:
INTEGRAL EQUATIONS AND OPERATOR THEORY
Editorial:
BIRKHAUSER VERLAG AG
Referencias:
Lugar: Basel, Switzerland; Año: 2014 vol. 80 p. 453 - 468
ISSN:
0378-620X
Resumen:
A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on C^n are hypercyclic. Moreover, it was shown by Bonilla and Grosse-Erdmann that they have frequently hypercyclic functions of exponential growth. On the other hand, in the infinite dimensional setting, the Godefroy?Shapiro theorem has been extended to several spaces of entire functions defined on Banach spaces. We prove that on all these spaces, non-trivial convolution operators are strongly mixing with respect to a gaussian probability measure of full support. For the proof we combine the results previously mentioned and we use techniques recently developed by Bayart and Matheron. We also obtain the existence of frequently hypercyclic entire functions of exponential growth.
