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SUMMARY:Polynomial approximation in a convex domain in $\\mathbb{C}^n$ whi
 ch is exponentially decreasing inside the domain
DTSTART;VALUE=DATE-TIME:20210701T144000Z
DTEND;VALUE=DATE-TIME:20210701T150000Z
DTSTAMP;VALUE=DATE-TIME:20260615T232945Z
UID:indico-contribution-215@indico.eimi.ru
DESCRIPTION:Speakers: Nikolai Shirokov (St.-Petersburg State University an
 d National Research University High School of Economics in SPb)\nLet $\\Om
 ega\\subset \\mathbb{C}^n$\, $n\\ge 2$\, be a bounded convex domain with t
 he $C^2$-smooth boundary. We suppose that $\\Omega$ satisfies some propert
 ies. The strictly convex in the analytical sense domains satisfy those pro
 perties. It is proved that for any function $f$ holomorphic is $\\Omega$ a
 nd 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 $\\Omega$.\n\nhttps://indico.eimi.ru/event/321/contributions/215/
LOCATION:
URL:https://indico.eimi.ru/event/321/contributions/215/
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