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Differentiable extensions of functions

Published in Differential Geometry and Its Applications. 1993, vol. 3, no. 1, p. 71 - 90
Abstract Those functions on arbitrary subsets of Image, which admit smooth extensions to Image, as well as those, which admit k-times differentiable extension having locally Lipschitzian derivatives, are characterized in terms of a simple boundedness condition on the difference quotients. In case of finite order differentiability also a continuous linear extension operator is constructed for the corresponding function spaces even for vector valued functions.
Keywords Extension of functionsconvenient vector spacesLipschitz conditiondifference quotientsinterpolation
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FROLICHER, Alfred, KRIEGL, Andréas. Differentiable extensions of functions. In: Differential Geometry and Its Applications, 1993, vol. 3, n° 1, p. 71 - 90. https://archive-ouverte.unige.ch/unige:12146

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Deposited on : 2010-10-19

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