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Abstract:

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.

Registro:

Documento: Artículo
Título:Hypercyclic homogeneous polynomials on H(C)
Autor:Cardeccia, R.; Muro, S.
Filiación:Departamento de Matemática-Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina; CONICET, Argentina
Palabras clave:Entire functions; Frequently hypercyclic operators; Homogeneous polynomials; Universal functions
Año:2018
Volumen:226
Página de inicio:60
Página de fin:72
DOI: http://dx.doi.org/10.1016/j.jat.2017.09.005
Título revista:Journal of Approximation Theory
Título revista abreviado:J. Approx. Theory
ISSN:00219045
CODEN:JAXTA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219045_v226_n_p60_Cardeccia

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Citas:

---------- APA ----------
Cardeccia, R. & Muro, S. (2018) . Hypercyclic homogeneous polynomials on H(C). Journal of Approximation Theory, 226, 60-72.
http://dx.doi.org/10.1016/j.jat.2017.09.005
---------- CHICAGO ----------
Cardeccia, R., Muro, S. "Hypercyclic homogeneous polynomials on H(C)" . Journal of Approximation Theory 226 (2018) : 60-72.
http://dx.doi.org/10.1016/j.jat.2017.09.005
---------- MLA ----------
Cardeccia, R., Muro, S. "Hypercyclic homogeneous polynomials on H(C)" . Journal of Approximation Theory, vol. 226, 2018, pp. 60-72.
http://dx.doi.org/10.1016/j.jat.2017.09.005
---------- VANCOUVER ----------
Cardeccia, R., Muro, S. Hypercyclic homogeneous polynomials on H(C). J. Approx. Theory. 2018;226:60-72.
http://dx.doi.org/10.1016/j.jat.2017.09.005