Bergmansche Integraloperatoren für instationäre Prozesse in der Ebene

Abstract

The complex integral operators of S. Bergman transform holomorphic functions of a complex variable into solutions of linear partial differential equations of elliptic type. In this way they make possible to construct explicitly these solutions and to study their properties by function-theoretic methods. We offer a generalization of Bergman’s operator method by which linear equations for time-dependent processes in the plane may be treated uniquely.