REDUCTION OF A LINEAR MATRIX OPERATOR OF DIFFERENTIATION IN MANY VARIABLES TO AN OPERATOR WITH AN ORDINARY DIFFERENTIATION OPERATOR

Abstract

Abstract. In the theory of equations with a linear partial differential operator of the first order, the question of differentiation and integration of vector functions is associated with considering them alternately along the characteristics of the operator, and the representation of their integrals by characteristics in the form of functions of many variables depended on the characteristic first integrals of the operator. The difficulty in this matter was to manage the characteristics and the first integrals for each of their variables so that they were in their places. Such control was implemented by projectors having pairwise ductile properties. The main results of this study are: 1) the use of the reduction method to reduce the matrix operator in partial derivatives to an operator with ordinary differentiations for one variable and 2) the use of projectors in matters of the composition of functions from many variables and the characteristics of the operator for each of the variables. These novelties of the research have a serious perspective.