Vol. 40, No. 2, 1972

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Approximation and interpolation

Arne Stray

Vol. 40 (1972), No. 2, 463–475

Let X be a compact plane set, X0 its interior, and suppose E is a subset of ∂X = XX0.H(X0) is the algebra of all bounded analytic functions on X0 and HE(X0) denotes all bounded continuous functions on X0 E analytic in X0.

Interpolation sets for HF(X0) are studied if E is open relative to ∂X.

If X satisfies certain conditions which involve analytic capacity, it is shown that an interpolation set S for H(X0) is an interpolation set for H(0) for some open set 0 which contains every point of X except the points on ∂X in the closure of S. Similar results are proved for R(X) without restrictions on X.

Mathematical Subject Classification
Primary: 30A82
Received: 9 December 1970
Published: 1 February 1972
Arne Stray
Mathematics Institute
University of Bergen
5007 Bergen