An outline of the theory of pseudoanalytic functions

Abstract

1. Introduction. Pseudoanalytic functions are, roughly speaking, solutions of generalized Cauchy-Riemann equations. Such functions were considered by Picard [67; 68] and by Beltrami [3; No comprehensive account is available in print and the main results have been announced only episodically and, in most cases, under unnecessarily restrictive hypotheses. In this paper we shall outline the main features of this theory.