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Aufspaltungen linearer gewöhnlicher Differentialoperatoren und der zugehörigen Greenschen Funktionen

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Abstract

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 Mk, 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 Mk to be singular.

Moreover, for special classes of operators the splittings can effectively be used for solving boundary value problems numerically.

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  1. Mathematisches Institut der Universität zu Köln, Weyertal 86-90, D-5000, Köln 41

    Ulrich Trottenberg

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  1. Ulrich Trottenberg
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Trottenberg, U. Aufspaltungen linearer gewöhnlicher Differentialoperatoren und der zugehörigen Greenschen Funktionen. Manuscripta Math 15, 289–308 (1975). https://doi.org/10.1007/BF01168680

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  • DOI: https://doi.org/10.1007/BF01168680

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