A natural counterpart of Vitushkin’s criterion is obtained in the problem of uniform approximation of functions by solutions of second-order homogeneous elliptic equations with constant complex coefficient on compact subsets of , . It is stated in terms of a single (scalar) capacity connected with the leading coefficient of the Laurent series. The scheme of approximation uses methods in the theory of singular integrals and, in particular, constructions of certain special Lipschitz surfaces and Carleson measures.

Bibliography: 23 titles.

中文翻译：

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通过具有恒定复数系数的二阶齐次椭圆型方程的解来确定各个函数的一致逼近的准则

Vitushkin判据的天然对应在由与上的紧凑子组恒定复数系数的二阶椭圆均匀方程解的功能一致逼近的问题得到，。它用与Laurent系列的前导系数有关的单个（标量）容量表示。逼近方案使用奇异积分理论中的方法，尤其是某些特殊Lipschitz曲面的构造和Carleson测度。

参考书目：23种。