Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions

A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on (Formula Presented.) 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...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Muro, Santiago, Pinasco, Damián
Publicado:	2014
Materias:	Convolution operators Frequently hypercyclic operators Holomorphy types Strongly mixing operators
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v80_n4_p453_Muro http://hdl.handle.net/20.500.12110/paper_0378620X_v80_n4_p453_Muro
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_0378620X_v80_n4_p453_Muro
record_format	dspace
spelling	paper:paper_0378620X_v80_n4_p453_Muro2023-06-08T15:40:27Z Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions Muro, Santiago Pinasco, Damián Convolution operators Frequently hypercyclic operators Holomorphy types Strongly mixing operators A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on (Formula Presented.) 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. © 2014, Springer Basel. Fil:Muro, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Pinasco, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v80_n4_p453_Muro http://hdl.handle.net/20.500.12110/paper_0378620X_v80_n4_p453_Muro
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Convolution operators Frequently hypercyclic operators Holomorphy types Strongly mixing operators
spellingShingle	Convolution operators Frequently hypercyclic operators Holomorphy types Strongly mixing operators Muro, Santiago Pinasco, Damián Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
topic_facet	Convolution operators Frequently hypercyclic operators Holomorphy types Strongly mixing operators
description	A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on (Formula Presented.) 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. © 2014, Springer Basel.
author	Muro, Santiago Pinasco, Damián
author_facet	Muro, Santiago Pinasco, Damián
author_sort	Muro, Santiago
title	Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
title_short	Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
title_full	Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
title_fullStr	Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
title_full_unstemmed	Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
title_sort	strongly mixing convolution operators on fréchet spaces of holomorphic functions
publishDate	2014
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v80_n4_p453_Muro http://hdl.handle.net/20.500.12110/paper_0378620X_v80_n4_p453_Muro
work_keys_str_mv	AT murosantiago stronglymixingconvolutionoperatorsonfrechetspacesofholomorphicfunctions AT pinascodamian stronglymixingconvolutionoperatorsonfrechetspacesofholomorphicfunctions
_version_	1768544553118203904

Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions

Ejemplares similares