Characterization of Mergelyan sets

Stray, A.

doi:10.1090/S0002-9939-1974-0361097-5

Characterization of Mergelyan sets
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Proc. Amer. Math. Soc. 44 (1974), 347-352 Request permission

Abstract:

Necessary and sufficient conditions on a relatively closed subset $F$ of $D = \{ z:|z| < 1\}$ are given such that each analytic function in $D$ which is uniformly continuous on $F$ can be uniformly approximated by polynomials on $K \cup F$ for each compact subset $K$ of $D$.

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