Hypercyclic convolution operators on Fréchet spaces of analytic 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 ho...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v336_n2_p1324_Carando http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v336_n2_p1324_Carando_oai |
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I28-R145-paper_0022247X_v336_n2_p1324_Carando_oai2020-10-19 Carando, D. Dimant, V. Muro, S. 2007 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. application/pdf http://hdl.handle.net/20.500.12110/paper_0022247X_v336_n2_p1324_Carando info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Anal. Appl. 2007;336(2):1324-1340 Convolution operators Hypercyclic operators Spaces of holomorphic functions Hypercyclic convolution operators on Fréchet spaces of analytic functions info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v336_n2_p1324_Carando_oai |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (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 |
Artículo Artículo publishedVersion |
| 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 |
| publishDate |
2007 |
| url |
http://hdl.handle.net/20.500.12110/paper_0022247X_v336_n2_p1324_Carando http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v336_n2_p1324_Carando_oai |
| work_keys_str_mv |
AT carandod hypercyclicconvolutionoperatorsonfrechetspacesofanalyticfunctions AT dimantv hypercyclicconvolutionoperatorsonfrechetspacesofanalyticfunctions AT muros hypercyclicconvolutionoperatorsonfrechetspacesofanalyticfunctions |
| _version_ |
1766026591822938112 |