A criterion for uniform approximability of individual functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients

Abstract

Abstract 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.