Pointwise bounded approximation by functions satisfying a side condition

Arne Stray

Vol. 51 (1974), No. 1, 301–305

DOI: 10.2140/pjm.1974.51.301

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 {f_n}_n=1^∞ of uniformly continuous analytic functions on D bounded by the sup norm of f and in addition satisfying sup{|f_n(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