Right inverses for linear, constant coefficient partial differential operators on distributions over open half spaces

Results of Hörmander on evolution operators together with a characterization of the present authors [Ann. Inst. Fourier, Grenoble 40, 619–655 (1990)] are used to prove the following: Let P ∈ ℂ[z1,...,zn] and denote by Pm its principal part. If P − Pm is dominated by Pm then the following assertions for the partial differential operators P(D) and Pm(D) are equivalent for N ∈ Sn−1:P(D) and/or Pm D)admit a continuous linear right inverse on C∞(H+(N)).P(D) admits a continuous linear right inverse on C∞ (ℝn) and a fundamental solution E ∈ C∞(ℝn) satisfying Supp \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$E \subset \overline {H - (N)} $$ \end{document}