Factorization of quasi-differential operators

Abstract

A quasi-differential generalization of operators of the form l n u = u ( n ) + p 1 u ( n − 1 ) + ⋯ + p n u {l_n}u = {u^{(n)}} + {p_1}{u^{(n - 1)}} + \cdots + {p_n}u is considered. This type of generalization was first formulated by M. Bôcher (1913). A result of A. Zettl (1971) giving a necessary and sufficient condition that a differential operator l n {l_n} be factorable into a product of lower order differential operators is extended to quasi-differential expressions.