Monge-Ampère Measures for Convex Bodies and Bernstein-Markov Type Inequalities

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dc.creatorBurns, D.
dc.creatorLevenberg, N.
dc.creatorMa'u, S.
dc.creatorRévész, Sz.
dc.date2007-05-08
dc.date.accessioned2026-07-07T08:00:00Z
dc.date.available2026-07-07T08:00:00Z
dc.descriptionWe use geometric methods to calculate a formula for the complex Monge-Ampère measure $(dd^cV_K)^n$, for $K \Subset \RR^n \subset \CC^n$ a convex body and $V_K$ its Siciak-Zaharjuta extremal function. Bedford and Taylor had computed this for symmetric convex bodies $K$. We apply this to show that two methods for deriving Bernstein-Markov-type inequalities, i.e., pointwise estimates of gradients of polynomials, yield the same results for all convex bodies. A key role is played by the geometric result that the extremal inscribed ellipses appearing in approximation theory are the maximal area ellipses determining the complex Monge-Ampère solution $V_K$.
dc.identifierhttps://arxiv.org/abs/0705.1095
dc.identifierhttp://arxiv.org/abs/0705.1095
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128581
dc.subjectComplex Variables
dc.subjectClassical Analysis and ODEs
dc.subject32U15
dc.titleMonge-Ampère Measures for Convex Bodies and Bernstein-Markov Type Inequalities
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