Failure of rational approximation on some Cantor type sets

Author:
Albert Mas-Blesa

Journal:
Proc. Amer. Math. Soc. **137** (2009), 635-640

MSC (2000):
Primary 30C85; Secondary 31A15

Published electronically:
June 20, 2008

MathSciNet review:
2448585

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the algebra of continuous functions on a compact set which are analytic on the interior of , and let be the closure (with respect to uniform convergence on ) of the functions that are analytic on a neighborhood of . A counterexample of a question posed by A. O'Farrell about the equality of the algebras and when , with and compact subsets of , is given. Also, the equality is proved with the assumption that has no interior.

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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

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09573-7

Keywords:
Rational approximation,
analytic capacity,
Cantor sets

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

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.