Rational approximation on the union of sets
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- by A. M. Davie and B. K. Øksendal PDF
- Proc. Amer. Math. Soc. 29 (1971), 581-584 Request permission
Abstract:
A counterexample is given to a conjecture of Val’skiǔ that if K is a compact plane set with interior U and the continuous function f on K satisfies $f|\bar U \in R(\bar U)$ and $f|bK \in R(bK)$ then $f \in R(K)$. The conjecture is shown to be true when U is a disc.References
- Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
- R. È. Val′skiĭ, Parts of algebras of analytic functions and measures orthogonal to these algebras, Sibirsk. Mat. Ž. 8 (1967), 1222–1235 (Russian). MR 0218902
Additional Information
- © Copyright 1971 American Mathematical Society
- 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