RIGHT INVERSES FOR LINEAR, CONSTANT COEFFICIENT PARTIAL-DIFFERENTIAL OPERATORS ON DISTRIBUTIONS OVER OPEN HALF-SPACES

Results of Hormander on evolution operators together with a characteri zation of the present authors [Arm. Inst. Fourier, Grenoble 40, 619-65 5 (1990)] are used to prove the following: Let P is an element of C[z( 1), ..., z(n)] and denote by P-m its principal part. If P - P-m is dom inated by P-m then the following assertions for the partial differenti al operators P(D) and P-m(D) are equivalent for N is an element of Sn- 1: (1) P(D) and/or P-m(D) admit a continuous linear right inverse on C -infinity (H+(N)). (2) P(D) admits a continuous linear right inverse o n C-infinity(R-n) and a fundamental solution E is an element of D-1(R- n) satisfying Supp E subset of <(H_(N))over bar>, where H+(N) := {x is an element of R-n :+/-[x, N] > 0}.