Sturdy Harmonic Functions and their Integral Representations

被引：0
作者：
Jürgen Bliedtner
Peter A. Loeb
机构：
[1] Universität Frankfurt,Fachbereich Mathematik
[2] University of Illinois at Urbana-Champaign,Department of Mathematics
来源：
Positivity | 2003年 / 7卷
关键词：
harmonic functions; integral representations; Dirichlet problem; Martin boundary; Choquet simplex;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Sturdy harmonic functions constitute all but the least tractable of the positive harmonic functions in potential-theoretic settings. They are the uniform limits on compact sets of positive, bounded harmonic functions and are also produced by a simple integral representation on the boundary of a natural compactification of the space on which they are defined. The boundary of that compactification is metrizable, and more regular for the Dirichlet problem, in general, than is the Martin boundary if that boundary is even defined in the setting.
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页码：355 / 387
页数：32
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