Arc-analytic roots of analytic functions are Lipschitz

DOI10.1090/S0002-9939-04-07323-XzbMath1043.32002MaRDI QIDQ4461154

Laurentiu Paunescu, Krzysztof Kurdyka

Publication date: 29 March 2004

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

analytic functionsLipschitz functionsarc-analytic maps

Mathematics Subject Classification ID

Semi-analytic sets, subanalytic sets, and generalizations (32B20) Nash functions and manifolds (14P20)

Related Items

Equivalence relations for two variable real analytic function germs ⋮ Bounds for zeros of entire functions ⋮ Hyperbolic polynomials and multiparameter real-analytic perturbation theory ⋮ Blow-analytic equivalence of two variable real analytic function germs ⋮ Equisingularity in \(\mathbb R^2\) as Morse stability in infinitesimal calculus

Cites Work

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• Arc-analytic functions
• On classification of real singularities
• Semianalytic and subanalytic sets
• On analytic function germs of two complex variables
• Ensembles semi-algébriques symétriques par arcs. (Semi-algebraic sets symmetric by arcs)
• Choosing roots of polynomials smoothly
• Racine carrée d'une fonction différentiable
• Sur un théorème de Glaeser
• A Function which is Arc-Analytic but not Continuous
• A counterexample to subanalyticity of an arc-analytic function
• An arc-analytic function with nondiscrete singular set
• Subanalytic Functions