Speaker
Nikolai Shirokov
(St.-Petersburg State University and National Research University High School of Economics in SPb)
Description
Let $\Omega\subset \mathbb{C}^n$, $n\ge 2$, be a bounded convex domain with the $C^2$-smooth boundary. We suppose that $\Omega$ satisfies some properties. The strictly convex in the analytical sense domains satisfy those properties. It is proved that for any function $f$ holomorphic is $\Omega$ and smooth in $\bar{\Omega}$ there exist polynomials $P_N$, $\deg P_N\leq N$ such that $\bigl|f(z)-P_N(z)\bigr|$ has the polynomial decay for $z\in \partial\Omega$ and the exponential decay when $z$ lies strictly inside $\Omega$.
Primary author
Nikolai Shirokov
(St.-Petersburg State University and National Research University High School of Economics in SPb)
