Linearly approximatable functions

De Pauw, Thierry; Koeller, Amos

doi:10.1090/S0002-9939-08-09667-6

Linearly approximatable functions
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by Thierry De Pauw and Amos Koeller

Proc. Amer. Math. Soc. 137 (2009), 1347-1356

DOI: https://doi.org/10.1090/S0002-9939-08-09667-6

Published electronically: October 6, 2008

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Abstract:

The notion of uniform linear approximatability generalizes that of being continuously differentiable. It occurs, e.g., in viscosity solutions of some degenerate partial differential equations. We establish the Hölder continuity of uniformly linearly approximatable functions, and we show that functions which are nowhere linearly approximatable form a residual collection of the appropriate Hölder space. Finally, we prove an analog of the implicit function theorem applied to level sets.

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