This paper deals with reduction of non-homogeneous linear systems of first order operator equations with constant coefficients. An equivalent reduced system, consisting of higher order linear operator equations having only one variable and first order linear operator equations in two variables, is obtained by using the rational canonical form.Key words: Linear system of first order operator equations with constant coefficients, n th order linear operator equation with constant coefficients, sum of principal minors, the rational canonical form, the characteristic polynomial
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.
Keywords:Linear system of first order operator equations with constant coefficients, n th order linear operator equation with constant coefficients, the characteristic polynomial, sum of principal minors, differential transcendency Email addresses : Branko Malešević , Dragana Todorić , Ivana Jovović , Sonja Telebaković
Abstract. In this paper we prove two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865-873], using a method for proving inequalities of mixed trigonometric polynomial functions.Mathematics subject classification (2010): 26D05.
We consider a total reduction of a nonhomogeneous linear system of operator equations with the system matrix in the companion form. Totally reduced system obtained in this manner is completely decoupled, i.e., it is a system with separated variables. We introduce a method for the total reduction, not by a change of basis, but by finding the adjugate matrix of the characteristic matrix of the system matrix. We also indicate how this technique may be used to connect differential transcendence of the solution with the coefficients of the system.
In this paper we will consider a partial reduction for nonhomogeneous linear systems of the operator equations with the system matrix in the companion form and with different operators. As a result of this method we will get an equivalent system consisting of the linear operator equations having only one or two variables. Homogeneous part of the equation in one unknown is obtained using generalized characteristic polynomial of the system matrix. We will also look more closely at some properties of the doubly companion matrix.
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