On a class of linear differential operators of first order with singular point

Abstract

The aim of this paper is to give a background to study spectral properties of some operators occurring in differentiall geometry. We deal with the problem of existence and uniqueness of local solutions of partial differential equations of type D[x]u — Bu = f. An integral formula for the solutions and conditions of its feasibility are given in terms of dynamics of the vector field X . A generalization to equations with polynomials in the operator D[x] is presented.