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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Convergence of Polynomial Level Sets
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by J. Ferrera PDF
Trans. Amer. Math. Soc. 350 (1998), 4757-4773 Request permission


In this paper we give a characterization of pointwise and uniform convergence of sequences of homogeneous polynomials on a Banach space by means of the convergence of their level sets. Results are obtained both in the real and the complex cases, as well as some generalizations to the nonhomogeneous case and to holomorphic functions in the complex case. Kuratowski convergence of closed sets is used in order to characterize pointwise convergence. We require uniform convergence of the distance function to get uniform convergence of the sequence of polynomials.
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Additional Information
  • J. Ferrera
  • Affiliation: Departmento Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, España
  • Email:
  • Received by editor(s): March 20, 1995
  • Additional Notes: Research partially supported by DGICYT grant PB-0044 (Spain).
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 4757-4773
  • MSC (1991): Primary 46E25; Secondary 12E05
  • DOI:
  • MathSciNet review: 1615959