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In this note we give some sharp estimates for norms of polynomials via the products of norms of their linear terms. Different convex norms on the unit disc are considered.

- A Kroó, D S Lubinsky
- 2012

We establish asymptotics for Christo¤el functions associated with multivariate orthogonal polynomials. The underlying measures are assumed to be regular on a suitable domain-in particular this is true if they are positive a.e on a compact set that admits analytic parametrization. As a consequence, we obtain asymptotics for Christo¤el functions for measures… (More)

- A Kroó, E B Saff, M Yattselev
- 2005

Remez-type inequalities provide upper bounds for the uniform norms of poly-nomials p on given compact sets K, provided that |p(x)| ≤ 1 for every x ∈ K \E, where E is a subset of K of small measure. In this paper we prove sharp Remez-type inequalities for homogeneous polynomials on star-like surfaces in R d. In particular, this covers the case of spherical… (More)

×ØÖÖØº Let P d n denote the set of real algebraic polynomials of d variables and of total degree at most n. For a compact set K ⊂ Ê d set P K = sup x∈K |P (x)|. d−1 Ó. (Here, as usual, S d−1 stands for the Eucledean unit sphere in Ê d .) Furthermore, given a smooth curve Γ ⊂ Ê d , we denote by D T P the tangential derivative of P along Γ (T is the unit… (More)

- András Kroó, E B Saff, Irwin Kra
- 2007

Let K be a compact set in the complex plane having connected and regular complement, and let / be any function continuous on K and analytic in the interior of K. For the polynomials pn(¡) of respective degrees at most n of best uniform approximation to / on K, we investigate the density of the sets of extreme points And) :={zeK: \f{z)-p*n{f)(z)\ =… (More)