Vol. 51, No. 1, 1974

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Pointwise bounded approximation by functions satisfying a side condition

Arne Stray

Vol. 51 (1974), No. 1, 301–305
Abstract

In this paper necessary and sufficient conditions on a subset S of the unit disc D are given such that every bounded analytic function f on D is a pointwise limit of a sequence {fn}n=1 of uniformly continuous analytic functions on D bounded by the sup norm of f and in addition satisfying sup{|fn(z)|,z ,S} sup{|f(z)|,z S} for all n.

Mathematical Subject Classification 2000
Primary: 30A82
Secondary: 46J15
Milestones
Received: 27 October 1972
Revised: 20 February 1973
Published: 1 March 1974
Authors
Arne Stray
Mathematics Institute
University of Bergen
5007 Bergen
Norway