Surjectivity of partial differential operators on ultradistributions of Beurling type in two dimensions

Abstract

We show that if ${\mit\Omega}$ is an open subset of $\mathbb R^2$, then the surjectivity of a partial differential operator $P(D)$ on the space of ultradistributions $\mathscr{D}'_{(\omega)}({\mit\Omega})$ of Beurling type is equivalent to the surjectivit