Arc-quasianalytic functions
Complex Variables
2014-01-31 v1 Classical Analysis and ODEs
Logic
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.
Cite
@article{arxiv.1401.7683,
title = {Arc-quasianalytic functions},
author = {Edward Bierstone and Pierre D. Milman and Guillaume Valette},
journal= {arXiv preprint arXiv:1401.7683},
year = {2014}
}
Comments
12 pages