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, S., Pinasco, D., Savransky, M.
Formato: JOUR
Materias:
Convolution operators
Frequently hypercyclic operators
Holomorphy types
Strongly mixing operators
Acceso en línea: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 todo:paper_0378620X_v80_n4_p453_Muro
record_format dspace
spelling todo:paper_0378620X_v80_n4_p453_Muro2023-10-03T15:33:13Z Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions Muro, S. Pinasco, D. Savransky, M. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, S.
Pinasco, D.
Savransky, M.
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.
format JOUR
author Muro, S.
Pinasco, D.
Savransky, M.
author_facet Muro, S.
Pinasco, D.
Savransky, M.
author_sort Muro, S.
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
url http://hdl.handle.net/20.500.12110/paper_0378620X_v80_n4_p453_Muro
work_keys_str_mv AT muros stronglymixingconvolutionoperatorsonfrechetspacesofholomorphicfunctions
AT pinascod stronglymixingconvolutionoperatorsonfrechetspacesofholomorphicfunctions
AT savranskym stronglymixingconvolutionoperatorsonfrechetspacesofholomorphicfunctions
_version_ 1807319658435444736

Ejemplares similares