Comparability of partial differential operators and manifold linearity

Abstract

The comparison of differential operators is a problem that was formulated in sixties by Lars Hormander, it is a part of the theory of partial differential operators with constant coefficients, this problem up to now does not have a complete solution.The urgency of this problem is stipulated by the applications of the solvability theory of differential equations in special spaces of generalized functions. In this paper we prove some results in the manifold linearity of a polynomial, these results play an important role in the comparison of two linear partial differential operators problem.