Analytic functions and Nash functions along curves

Bibliographic description

punktacja MEiN [2023]: 140

title:	Analytic functions and Nash functions along curves
author:	Kucharz Wojciech , Kurdyka Krzysztof
journal title:	Selecta Mathematica. New Series
volume:	29
issue:	1
date of publication :	2023
article ID:	16
ISSN:	1022-1824
eISSN:	1420-9020
DOI:	10.1007/s00029-022-00824-9
language:	English
journal language:	English
abstract in English:	Let $X$ be a real analytic manifold. A function $f$ : $X \rightarrow \mathbb{R}$ is said to be curve-analytic if it is real analytic when restricted to any locally irreducible real analytic curve in $X$. We prove that every curve-analytic function with subanalytic graph is actually real analytic. To accomplish this task, we give a criterion for an arc-analytic function to be real analytic. A function is called arc-analytic if it is real analytic along any parametric real analytic arc. We also obtain analogous results for Nash manifolds and Nash functions, in which case the assumption of subanalyticity is superfluous.
keywords in English:	real analytic function, arc-analytic function, subanalytic function, Nash function, arc-Nash function
affiliation:	Wydział Matematyki i Informatyki : Instytut Matematyki
type:	journal article
subtype:	academic paper