Differential operators of constant strength

Abstract

We have seen in Chapter VI that existence theorems for differential operators with variable coefficients must require some conditions besides smoothness of the coefficients. In this chapter we shall study differential operators which in the spaces ℬ _{p, k} can be considered as bounded perturbations of differential operators with constant coefficients; we call them differential operators of constant strength. Most of the results which we have proved for differential operators with constant coefficients can be extended locally to differential operators of constant strength by means of a simple perturbation argument.