Vol. 35, No. 2, 1970

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An approximation theorem for subalgebras of H∞

Arne Stray

Vol. 35 (1970), No. 2, 511–515
Abstract

Let E be a closed subset of the unitcircle T = {z : |z| = 1} and denote by BE the algebra of all functions which are bounded and continuous on the set X = {z : |z|1&zE} and analytic in D = {z : |z| < 1}.

The main result of this paper (Theorem 1) is that there exist an open set V E containing X such that every f BE can be approximated uniformly on X by functions being analytic in V E.

Mathematical Subject Classification
Primary: 46.55
Milestones
Received: 30 December 1969
Published: 1 November 1970
Authors
Arne Stray
Mathematics Institute
University of Bergen
5007 Bergen
Norway