Factorization of disconjugate higher-order Sturm-Liouville difference operators

Using a recently proved equivalence between disconjugacy of the 2n(th)-orde r difference equation L(y)(k+n) := (nu=0)Sigma(n)(-1)(nu)Delta(nu)(r(k)((nu))Delta(nu)y(k+n-nu)) = 0, and solvability of the corresponding Riccati matrix difference equation, it is shown that the equation L(y) = 0 is disconjugate on a given interval if and only if the operator L admits the factorization of the form L(y)(k+n) = M*(c(k)M(y)(k))(k+n), where M and its adjoint M* are certain n(th)-order difference operators and ck is a sequence of positive numbers. (C) 1998 Elsevier Science Ltd. All r ights reserved.