Approximation of pseudoanalytic functions on the unit disk

Abstract

Pseudoanalytic functions F are constructed as complex combinations of real-valued analytic solutions of a generalized Stokes-Beltrami system. Function-theoretic methods identify the radius of the maximal open disk of analyticity of F, and the growth of F at its boundary from local pseudoanalytic polynomial approximates in the sense of S. N. Bernstein's classical theorem in analytic function theory.