On polynomial solutions of PDE

Abstract

In this paper we prove that the PDE $p(D)f=q,$ where $p$ and $q$ are multivariate polynomials, has a solution in the space of polynomials of total degree not exceeding $n+s,$ where $n$ is the degree of $q$ and $s$ is the zero order of $O=(0,\dots ,0)$ for $p.$

8 pages