Arc-analytic roots of analytic functions are Lipschitz |
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Authors: | Krzysztof Kurdyka Laurentiu Paunescu |
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Affiliation: | Laboratoire de Mathématiques (LAMA), Université de Savoie, UMR 5127 CNRS, 73-376 Le Bourget-du-Lac cedex, France ; School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia |
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Abstract: | Let be an arc-analytic function (i.e., analytic on every analytic arc) and assume that for some integer the function is real analytic. We prove that is locally Lipschitz; even if is less than the multiplicity of . We show that the result fails if is only a , arc-analytic function (even blow-analytic), . We also give an example of a non-Lipschitz arc-analytic solution of a polynomial equation , where are real analytic functions. |
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Keywords: | Real analytic subanalytic arc-analytic Lipschitz |
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