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arXiv · 1401.7683

Arc-quasianalytic functions

Edward Bierstone·Pierre D. Milman·Guillaume Valette
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Abstract

We work with quasianalytic classes of functions. Consider a real-valued function y = f(x) on an open subset U of Euclidean space, which satisfies a quasianalytic equation G(x, y) = 0. We prove that f is arc-quasianalytic (i.e., its restriction to every quasianalytic arc is quasianalytic) if and only if f becomes quasianalytic after (a locally finite covering of U by) finite sequences of local blowing-ups. This generalizes a theorem of the first two authors on arc-analytic functions.

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Edward Bierstone, Pierre D. Milman, Guillaume Valette. 2014-01-29. Arc-quasianalytic functions. https://arxiv.org/abs/1401.7683

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