A GENERALIZATION OF DOUGLIS-NIRENBERG ELLIPTIC OPERATORS

摘要

It is well known that the composition of two elliptic differential operators of orders ω and is ω~1again an elliptic operator of order ω + ω~1. This fact is not true for the composition of two multi-order systems elliptic in the sense of Doughs and Nirenberg. We consider a new more general class of multi-order pseudodifferential operators. This class of multi-order essentially elliptic operators is closed with respect to the composition, coordinate and basis transformation. Moreover, every multi-order essentially elliptic operator hasa parametrix belonging to the class and therefore is a Fredholm operator.