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