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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Failure of rational approximation on some Cantor type sets
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by Albert Mas-Blesa PDF
Proc. Amer. Math. Soc. 137 (2009), 635-640 Request permission

Abstract:

Let $A(K)$ be the algebra of continuous functions on a compact set $K\subset \mathbb {C}$ which are analytic on the interior of $K$, and let $R(K)$ be the closure (with respect to uniform convergence on $K$) of the functions that are analytic on a neighborhood of $K$. A counterexample of a question posed by A. O’Farrell about the equality of the algebras $R(K)$ and $A(K)$ when $K=(K_{1}\times [0,1])\cup ([0,1]\times K_{2})\subseteq \mathbb {C}$, with $K_{1}$ and $K_{2}$ compact subsets of $[0,1]$, is given. Also, the equality is proved with the assumption that $K_{1}$ has no interior.
References
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Additional Information
  • Albert Mas-Blesa
  • Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
  • Email: amblesa@mat.uab.cat
  • Received by editor(s): February 6, 2008
  • Published electronically: June 20, 2008
  • Additional Notes: This work was supported by grant AP2006-02416 (Programa FPU del MEC, España), and also partially supported by grants 2005SGR-007749 (Generalitat de Catalunya) and MTM2007-62817 (MEC, España)
  • Communicated by: Mario Bonk
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 635-640
  • MSC (2000): Primary 30C85; Secondary 31A15
  • DOI: https://doi.org/10.1090/S0002-9939-08-09573-7
  • MathSciNet review: 2448585