Nullspaces, representations and factorizations of quasi-differential expressions

Abstract

We consider quasi-differential expressions having matrix-valued coefficients on a real interval I. Certain general properties are proved which are new even in the case of scalar expressions.In particular, it is shown in the scalar case (i) that, if two expressions M1 and M2 have the same null space, then M1 = f M2 for some suitable function f and that (ii) if two coefficient matrices A, B E Zn(I) generate the same nth order expression then the product of the elements above the leading diagonal is the same for A and B. These properties are used to further prove new results concerning the factorization of scalar expressions.

Locations

• Differential and Integral Equations - View - PDF