SOME REMARKS ON QUASI-DIFFERENTIAL EXPRESSIONS WITH MATRIX-VALUED COEFFICIENTS

Abstract

This paper is Concerned with the relationship between ordinary linear quasi-differential expressions, defined in terms of locally Lebesgue integrable matrix coefficients given on an interval of the real line and “Classical” differential expressions with smooth (differentiable to certain prescribed orders) matrix coefficients. This relationship wan investigated in a recent paper of Everitt and Race [1] for the case of scalar quasi-differential expressions of Shin-Zettl type. The present work extends the ideas given there, to the more general quasi-differential expressions considered by Frentzen in recent years (see, for example [4,5]) and applies them to products and polynomials of expressions.