Criterion of uniform approximability by harmonic functions on compact sets in a"e3

被引：6
|
作者：
Mazalov, M. Ya. [1 ]
机构：
[1] Moscow Power Engn Inst, Smolensk Branch, Smolensk 214013, Russia
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2012年 / 279卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
APPROXIMATION;
D O I：
10.1134/S008154381208010X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For a function continuous on a compact set X aS, a"e(3) and harmonic inside X, we obtain a criterion of uniform approximability by functions harmonic in a neighborhood of X in terms of the classical harmonic capacity. The proof is based on an improved localization scheme of A.G. Vitushkin, on a special geometric construction, and on the methods of the theory of singular integrals. DOI: 10.1134/S008154381208010X
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页码：110 / 154
页数：45
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