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
14h00 - 15h00
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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