Real roots of polynomials and right inverses for partial differential operators in the space of tempered distributions
Michael Langenbruch · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1990
Synopsis LetP(D)be a partial differential operator with constant coefficients. IfP(D)has a continuous linear right inverse in the space of tempered distributions, thenPis the product of a polynomial without real roots and a real polynomial admitting a right inverse. If the polynomialPis real and irreducible, thenP(D)admits a right inverse in the tempered distributions if and only ifP(×)has the property of zeros of R. Thorn.