Factorization of disconjugate higher-order Sturm-Liouville difference operators

Using a recently proved equivalence between disconjugacy of the 2nth-order difference equation 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*(ckM(y)k)k+n, where M and its adjoint M* are certain nth-order difference operators and ck is a sequence of positive numbers