On Domination Conditions for Systems of Minimal Differential Operators Acting in the Space L ∞ $$\mathbb{R}^n $$

In this paper, we consider the linear space of minimal differential operators with constant coefficients which are dominated by systems of minimal operators acting in spaces with uniform norm. In terms of domination conditions, we prove the quasiellipticity test for a given operator; this criterion generalizes a similar result of De Leeuw and Mirkil to elliptic operators.