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arXiv · 1310.8455

Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems

Anja Korporal·Georg Regensburger
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Abstract

We consider solution operators of linear ordinary boundary problems with "too many" boundary conditions, which are not always solvable. These generalized Green's operators are a certain kind of generalized inverses of differential operators. We answer the question when the product of two generalized Green's operators is again a generalized Green's operator for the product of the corresponding differential operators and which boundary problem it solves. Moreover, we show that---provided a factorization of the underlying differential operator---a generalized boundary problem can be factored into lower order problems corresponding to a factorization of the respective Green's operators. We illustrate our results by examples using the Maple package IntDiffOp, where the presented algorithms are implemented.

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BibTeXRIS

Anja Korporal, Georg Regensburger. 2013-10-31. Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems. https://doi.org/10.1007/978-3-642-54479-8_5

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