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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Chaotic polynomials on Fréchet spaces
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by Alfredo Peris PDF
Proc. Amer. Math. Soc. 127 (1999), 3601-3603 Request permission

Erratum: Proc. Amer. Math. Soc. 129 (2001), 3759-3760.


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 $\mathcal {H}(\mathbb {C} )$.
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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:
  • 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
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3601-3603
  • MSC (1991): Primary 46G20, 46A04, 58F08
  • DOI:
  • MathSciNet review: 1610769