On Bernstein-Markov Property for Multivariate Polynomials

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• Andras Kroo (Renyi Institute for Mathematics, Hungarian Academy of Sciences)
• Friday 19 July 2024, 11:30-12:10
• Seminar Room 1, Newton Institute.

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DREW01 - Multivariate approximation, discretization, and sampling recovery

The primary goal of this talk is to present new general conditions which ensure that Bernstein-Markov property holds in multivariate setting. The Bernstein-Markov property of multivariate polynomials is equivalent to subexponential increase of Nikolskii type upper bounds (or subexponential decrease of  Christoffel functions). We will introduce a rather general property of points (domains) being weakly analytically connected which will turn out to be sufficient for the Bernstein-Markov property to hold for every positive a.e. weight. In addition, we will use the same method in order to verify subexponential increase of derivatives of multivariate polynomials and continuity of the multivariate Siciak extremal function.  Explicit quantitative estimates will be proveded which in some particular cases will yield bounds of polynomial order.

This talk is part of the Isaac Newton Institute Seminar Series series.

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