Smooth approximation in polynomially bounded o-minimal structures
Speaker: Xuan Viet Nhan Nguyen (BCAM, Spain)

Time: 15h15, Friday, 14/1/20212

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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.

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