Speaker: Xuan Viet Nhan Nguyen (BCAM, Spain)
Time: 15h15, Friday, 14/1/20212
Join Zoom Meeting
https://us02web.zoom.us/j/89603210669?pwd=dDJyYnJHd3A5WlR1cFFkRUlYa3loUT09
Meeting ID: 896 0321 0669
Passcode: 340252
Abstract: Let $f: mathbb{R}^n to mathbb{R}$ be a $C^p$ semialgebraic function , $p in mathbb{N}$. Shiota (1986) proved that given a positive continuous semi-algebraic function $varepsilon: mathbb{R}^n to mathbb{R}$, there is a $C^infty$ semialgebraic function $g: mathbb{R}^n to mathbb{R}$ such that $|D^alpha (f - g)| < varepsilon$ for every $|alpha|leq p$. In this talk, we show that the theorem still holds if we replace semialgebraic functions by definable functions in polynomially bounded o-minimal structures that allow smooth cell decompositions. Some applications are also given. This is a joint work with Anna Valette.
For general information of the AGEA seminar, please check out
https://sites.google.com/ncts.ntu.edu.tw/agea-seminar
or the mirror site
http://www.math.ntu.edu.tw/~jkchen/agea-seminar.html | 
