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Linear equations depending differentiably on a parameter

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Abstract

We investigate operator functionsT(x) inBanach spaces, depending differentiably (meaning of classC μ orC ∞) on a parameterx and enjoying a certain “regularity property”. Iff is a given differentiable function such that the equationT(x)e=f(x) is solvable for eachx then the existence of a functione is proved which belongs to the same differentiability class asf andT, solving the equationT(x)e(x)≡f(x) identically inx. As an application we extend a result ofJ. Leiterer [9] and give a comprehensive answer to a question posed byJ.L. Taylor in [15] concerning the exactness of certain cochain complexes.

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  1. Abteilung Mathematik, Universität Dortmund, Postfach 500500, D-4600, Dortmund 50

    Frank Mantlik

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  1. Frank Mantlik
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Mantlik, F. Linear equations depending differentiably on a parameter. Integr equ oper theory 13, 231–250 (1990). https://doi.org/10.1007/BF01193758

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