Normal forms of linear second order partial differential equations on the plane

Abstract

The paper is devoted to the theory of normal forms of main symbols for linear second order partial differential equations on the plane. We discuss the results obtained in the last decades and some problems, which are important both for the development of this theory and the applications. The reduction theorem, which was used to obtain many of recent results in the theory, is included in the paper in the parametric form together with proof. There is a feeling that the theorem still has potential to get progress in the solution of open problems in the theory.