Best Harmonic and Superharmonic L¹-Approximants in Strips

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In this Subject: <a title="Mathematics and Statistics" href="/content/subcat?j_subject=195&j_availability=">Mathematics and Statistics
By this author: Armitage D.H. ;&nbsp; Golitschek S.M.J.

Authors: Armitage D.H.; Golitschek S.M.J.

Source: Journal of Approximation Theory, Volume 100, Number 2, October 1999 , pp. 266-283(18)

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Abstract:

Let denote the open strip (-1, 1)× Ropf ^n-1, where n ges 2. We completely solve the problem of characterizing a best harmonic L¹-approximant to a subharmonic function s on (all functions are assumed to be continuous and integrable on ¯). This characterization was previously known only under highly restrictive hypotheses on s. The approach of this paper is based, in part, on ideas used recently to solve the corresponding problem for the unit ball. However, the unboundedness of presents difficulties which require the use of new techniques and recent results from other branches of harmonic approximation theory. Superharmonic L¹-approximation of subharmonic functions is also treated. Copyright 1999 Academic Press.