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Proceedings of the American Mathematical Society

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

 

 

Rational approximation on the union of sets


Authors: A. M. Davie and B. K. Øksendal
Journal: Proc. Amer. Math. Soc. 29 (1971), 581-584
MSC: Primary 30.70
DOI: https://doi.org/10.1090/S0002-9939-1971-0277725-6
MathSciNet review: 0277725
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Abstract: A counterexample is given to a conjecture of Val'skiu that if K is a compact plane set with interior U and the continuous function f on K satisfies $ f\vert\bar U \in R(\bar U)$ and $ f\vert bK \in R(bK)$ then $ f \in R(K)$. The conjecture is shown to be true when U is a disc.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0277725-6
Keywords: Compact plane set, rational approximation, $ {T_\varphi }$ operator, analytically negligible set
Article copyright: © Copyright 1971 American Mathematical Society