Hypercyclic convolution operators on Fréchet spaces of analytic functions

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A result of Godefroy and Shapiro states that the convolution operators on the space of entire functions on Cn, which are not multiples of identity, are hypercyclic. Analogues of this result have appeared for some spaces of holomorphic functions on a Banach space. In this work, we define the space ho...

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Autores principales: Carando, D., Dimant, V., Muro, S.
Formato: JOUR
Materias:
Convolution operators
Hypercyclic operators
Spaces of holomorphic functions
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v336_n2_p1324_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_0022247X_v336_n2_p1324_Carando
record_format dspace
spelling todo:paper_0022247X_v336_n2_p1324_Carando2023-10-03T14:29:12Z Hypercyclic convolution operators on Fréchet spaces of analytic functions Carando, D. Dimant, V. Muro, S. Convolution operators Hypercyclic operators Spaces of holomorphic functions A result of Godefroy and Shapiro states that the convolution operators on the space of entire functions on Cn, which are not multiples of identity, are hypercyclic. Analogues of this result have appeared for some spaces of holomorphic functions on a Banach space. In this work, we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators. Some known results come out as particular cases of this setting. We also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the Schatten-von Neumann class. © 2007 Elsevier Inc. All rights reserved. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Dimant, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Muro, S. 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_0022247X_v336_n2_p1324_Carando
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
Hypercyclic operators
Spaces of holomorphic functions
spellingShingle Convolution operators
Hypercyclic operators
Spaces of holomorphic functions
Carando, D.
Dimant, V.
Muro, S.
Hypercyclic convolution operators on Fréchet spaces of analytic functions
topic_facet Convolution operators
Hypercyclic operators
Spaces of holomorphic functions
description A result of Godefroy and Shapiro states that the convolution operators on the space of entire functions on Cn, which are not multiples of identity, are hypercyclic. Analogues of this result have appeared for some spaces of holomorphic functions on a Banach space. In this work, we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators. Some known results come out as particular cases of this setting. We also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the Schatten-von Neumann class. © 2007 Elsevier Inc. All rights reserved.
format JOUR
author Carando, D.
Dimant, V.
Muro, S.
author_facet Carando, D.
Dimant, V.
Muro, S.
author_sort Carando, D.
title Hypercyclic convolution operators on Fréchet spaces of analytic functions
title_short Hypercyclic convolution operators on Fréchet spaces of analytic functions
title_full Hypercyclic convolution operators on Fréchet spaces of analytic functions
title_fullStr Hypercyclic convolution operators on Fréchet spaces of analytic functions
title_full_unstemmed Hypercyclic convolution operators on Fréchet spaces of analytic functions
title_sort hypercyclic convolution operators on fréchet spaces of analytic functions
url http://hdl.handle.net/20.500.12110/paper_0022247X_v336_n2_p1324_Carando
work_keys_str_mv AT carandod hypercyclicconvolutionoperatorsonfrechetspacesofanalyticfunctions
AT dimantv hypercyclicconvolutionoperatorsonfrechetspacesofanalyticfunctions
AT muros hypercyclicconvolutionoperatorsonfrechetspacesofanalyticfunctions
_version_ 1782029526114500608

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