Efroymson’s Approximation Theorem for globally subanalytic functions

Anna Valette
Jagiellonian University, Kraków, Poland
https://apacz.matinf.uj.edu.pl/users/245-anna-valette

Date(s) : 15/04/2021   iCal
14 h 00 min - 15 h 00 min

Efroymson’s Approximation Theorem asserts that if f is a continuous semialgebraic mapping on a C^infinity semialgebraic submanifold M of ℝⁿ and if e : M→ℝ is a positive continuous semialgebraic function then there is a C^infinity semialgebraic function g:M→ℝ such that |f-g|<e. The aim of this talk is to give some insights into the proof of generalized Efroymson’s theorem to the globally subanalytic category.

Our framework is however much bigger than this category since our approximation theorems hold on every polynomially bounded o-minimal structure expanding the real field that admits C^infinity cell decomposition. In particular, it applies to quasi-analytic Denjoy-Carleman classes.

Work in collaboration with Guillaume Valette.

https://arxiv.org/abs/1905.05703

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