Video library: A. S. Sadullaev, Polynomial approximation on algebraic variety

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International Conference on Complex Analysis Dedicated to the Memory of Andrei Gonchar and Anatoliy Vitushkin November 21, 2023 15:00, Steklov Institute, conference hall, 9th floor

Polynomial approximation on algebraic variety A. S. Sadullaev Urgench State University named after Al-Khorezmi
https://youtu.be/sI3IMzVJutg Abstract: The talk is devoted to the discussion of the following problem: let $A\subset \mathbb C^N$, $\operatorname{dim}A=n$, be an algebraic variety, $f(z)\in C(K)$ be some continuous function on a compact set $K\subset A$. If the approximation rate $$ \varlimsup_{m\to\infty}\rho_m^{1/m}(f,K)=\delta<1. $$ where $\rho_m(f,K)=\min\{\\|f-p_m\\|_K, \operatorname{deg}p_m\leq{m}\}$ is the minimal deviation of $f$ from polynomials $p_m$ of degree $\leq{m}$, then what can we say about analyticity of $f$ in a neighborhood of the compact set $K$ ? Website: https://zoom.us/j/98008001815?pwd=OG1rTVRFRzFpY3RhZmE4MXFwckxMUT09 ^* ID: 980 0800 1815; Password: 055016