Some sufficient conditions for the comparability of two differential operators

Abstract

The comparison of differential operators is a problem of the theory of partial differential operators with constant coefficients. This problem up to now doesn't have a complete solution. It was formulated in the sixties by Lars Hormander in his monograph "The Analysis of Linear Partial Differential Operators". Many facts of the theory of partial differential equations can be formulated by using the concept of pre-order relation over the set of differential operators, however it is too complicated to check the comparability condition of two differential operators. In this paper we get some sufficient conditions for the comparability of two differential operators.

Comparability of partial differential operators and manifold linearity

“…Dif f C (n, m) is by definition the set of all linear partial differential operators with constant complex coefficients. Definition 1.1 [2,5] Hormander's function of the polynomial P (ξ) is called the function P (ξ) defined by the formula (1.4)…”