Existence and approximation of solutions of differential equations

Abstract

In the theory of differential operators with constant coefficients developed in this chapter and the next, the existence of a fundamental solution proved in section 3.1 has a central place. This result was first obtained in full generality by Ehrenpreis [1] and by Malgrange [1]. Our proof follows that of Malgrange [1] with the modifications introduced by Hörmander [2] in order to obtain the best possible local regularity properties. This improvement is necessary for the passage to operators with variable coefficients in Chapter VII and for the study of interior regularity properties in Chapter IV.