Abstract
The paper deals with the problem of factorization of a linear differential operator with matrix-valued coefficients into a product of lower order operators of the same type. Necessary and sufficient conditions for the factorization of the considered operator are given. These conditions are obtained by using the integral manifolds approach. Some consequences of the obtained results are also considered.MSC:34A30, 47A50, 47E05.
Highlights
Factorization of differential and difference operators uses analogies between these operators and algebraic polynomials
A linear differential operator L admits factorization if it can be represented as a product of lower order operators of the same type
We focus on an nth order linear differential operator of the form n
Summary
Factorization of differential and difference operators uses analogies between these operators and algebraic polynomials. Splitting equations Let us consider the linear differential equation of order n, formed by acting the operator ( ) on a vector function Z: n– Suppose that the linear system of differential equations ( ) has an integral manifold defined by the vector equation of the form
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