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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Chaotic polynomials on Fréchet spaces


Author: Alfredo Peris
Journal: Proc. Amer. Math. Soc. 127 (1999), 3601-3603
MSC (1991): Primary 46G20, 46A04, 58F08
Published electronically: May 13, 1999
Erratum: Proc. Amer. Math. Soc. (recently posted)
MathSciNet review: 1610769
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Abstract: Contrary to the case of polynomials on Banach spaces, in which it is known that no hypercyclic homogeneous polynomial of degree $m \geq 2$ exists on any Banach space, we construct for each $m \geq 2$ a chaotic $m$-homogeneous polynomial $P$ on the Fréchet space ${\cal H}(\mathbb C)$.


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Additional Information

Alfredo Peris
Affiliation: Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain
Email: aperis@pleiades.upv.es

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04937-0
PII: S 0002-9939(99)04937-0
Received by editor(s): December 29, 1997
Received by editor(s) in revised form: February 17, 1998
Published electronically: May 13, 1999
Additional Notes: This research was supported in part by DGICYT under Proyecto PB94-0541.
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society