Aufspaltungen linearer gewöhnlicher Differentialoperatoren und der zugehörigen Greenschen Funktionen

Let M be a regular linear ordinary differential operator of the n-th order, associated with certain homogeneous boundary conditions. Suppose that M is invertable. We provide sufficient conditions to split M into a product of lower order operators M_k, which may be singular at the endpoints of the given interval. To these splittings-which depend on the given boundary conditions-there corresponds a splitting of the associated Green's function. The results are applied in the theory of inverse-positive operators and the theory of totally positive Green's functions. These applications, in general, require the operators M_k to be singular. Moreover, for special classes of operators the splittings can effectively be used for solving boundary value problems numerically.