Smooth approximation in polynomially bounded o-minimal structures
Người trình bày: Nguyễn Xuân Việt Nhân (Basque Center for Applied Mathematics, Spain)

Thời gian: 14h00, thứ ba, ngày 21/12/2021.

Hình thức: Trực tuyến link google meet: meet.google.com/zsh-jnxc-eit


Tóm tắt: Let $f: mathbb{R}^n to mathbb{R}$ be a $C^p$ semialgebraic function , $p in mathbb{N}$. Shiota (1986) proved that for a positive continuous semi-algebraic function $varepsilon: mathbb{R}^n to mathbb{R}$, there is a $C^infty$ semialgebraic function $g: mathbb{R}^b to mathbb{R}$ such that $|D^alpha (f - g)| < varepsilon$ for every $|alpha|leq p$. In this talk, we show that the theorem holds true if we replace semialgebraic functions with 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.



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