Hypercyclic homogeneous polynomials on H(C)

It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fréchet spaces. We show the existence of hypercyclic polynomials on H(C), by exhibiting a concrete polynomial which is also the first ex...

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Autores principales: Cardeccia, R., Muro, S.
Formato: JOUR
Materias:
Entire functions
Frequently hypercyclic operators
Homogeneous polynomials
Universal functions
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00219045_v226_n_p60_Cardeccia
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00219045_v226_n_p60_Cardeccia
record_format dspace
spelling todo:paper_00219045_v226_n_p60_Cardeccia2023-10-03T14:22:39Z Hypercyclic homogeneous polynomials on H(C) Cardeccia, R. Muro, S. Entire functions Frequently hypercyclic operators Homogeneous polynomials Universal functions It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fréchet spaces. We show the existence of hypercyclic polynomials on H(C), by exhibiting a concrete polynomial which is also the first example of a frequently hypercyclic homogeneous polynomial on any F-space. We prove that the homogeneous polynomial on H(C) defined as the product of a translation operator and the evaluation at 0 is mixing, frequently hypercyclic and chaotic. We prove, in contrast, that some natural related polynomials fail to be hypercyclic. © 2017 Elsevier Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00219045_v226_n_p60_Cardeccia
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Entire functions
Frequently hypercyclic operators
Homogeneous polynomials
Universal functions
spellingShingle Entire functions
Frequently hypercyclic operators
Homogeneous polynomials
Universal functions
Cardeccia, R.
Muro, S.
Hypercyclic homogeneous polynomials on H(C)
topic_facet Entire functions
Frequently hypercyclic operators
Homogeneous polynomials
Universal functions
description It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fréchet spaces. We show the existence of hypercyclic polynomials on H(C), by exhibiting a concrete polynomial which is also the first example of a frequently hypercyclic homogeneous polynomial on any F-space. We prove that the homogeneous polynomial on H(C) defined as the product of a translation operator and the evaluation at 0 is mixing, frequently hypercyclic and chaotic. We prove, in contrast, that some natural related polynomials fail to be hypercyclic. © 2017 Elsevier Inc.
format JOUR
author Cardeccia, R.
Muro, S.
author_facet Cardeccia, R.
Muro, S.
author_sort Cardeccia, R.
title Hypercyclic homogeneous polynomials on H(C)
title_short Hypercyclic homogeneous polynomials on H(C)
title_full Hypercyclic homogeneous polynomials on H(C)
title_fullStr Hypercyclic homogeneous polynomials on H(C)
title_full_unstemmed Hypercyclic homogeneous polynomials on H(C)
title_sort hypercyclic homogeneous polynomials on h(c)
url http://hdl.handle.net/20.500.12110/paper_00219045_v226_n_p60_Cardeccia
work_keys_str_mv AT cardecciar hypercyclichomogeneouspolynomialsonhc
AT muros hypercyclichomogeneouspolynomialsonhc
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