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SUMMARY:On Bernstein-Markov Property for Multivariate Polynomials - Andras
   Kroo (Renyi Institute for Mathematics\, Hungarian Academy of Sciences)
DTSTART:20240719T103000Z
DTEND:20240719T111000Z
UID:TALK218200@talks.cam.ac.uk
DESCRIPTION:The primary goal of this talk is to present new general condit
 ions which ensure that Bernstein-Markov property holds in multivariate set
 ting. The Bernstein-Markov property of multivariate polynomials is equival
 ent to subexponential increase of Nikolskii type upper bounds (or subexpon
 ential decrease of&nbsp\; Christoffel functions). We will introduce a rath
 er general property of points (domains) being weakly analytically connecte
 d which will turn out to be sufficient for the Bernstein-Markov property t
 o hold for every positive a.e. weight. In addition\, we will use the same 
 method in order to verify subexponential increase of derivatives of multiv
 ariate polynomials and continuity of the multivariate Siciak extremal func
 tion.&nbsp\; Explicit quantitative estimates will be proveded which in som
 e particular cases will yield bounds of polynomial order.
LOCATION:Seminar Room 1\, Newton Institute
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