Differential transcendency in the theory of linear differential systems with constant coefficients

Abstract

In this paper we consider a reduction of a non-homogeneous linear system of first order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant coefficients and to the question of differential transcendency.

Key words: Sums of principal minors, the characteristic polynomial, linear system of first order operator equations with constant coefficients, n-th order linear operator equation with constant coefficients, operator generalization of Cramer's rule, formulae of total reduction for linear systems of first order operator equations, http://www.hindawi.com/isrn/ma/2012/403983/