Über funktionentheoretische Eigenschaften der Lösungen gewisser elliptischer Differentialgleichungen

Abstract

Some function theoretic properties of the solutions of the elliptic differential equation $w_{z,\bar{z}}+a(z,\bar{z})w_{\bar{z}}+b(z,\bar{z})w=0$ are discussed which can be represented by differential operators of K. W. Bauer. After a discussion of general properties, formal powers are defined. With this it is possible to prove some theorems essential in the classical theory of functions for certain subclasses of the solutions of this equation which are generalizations of holomorphic functions.