Sharp Constants of Approximation Theory. III. Certain Polynomial Inequalities of Different Metrics on Convex Sets

Michael I. Ganzburg

doi:10.1016/j.jat.2019.105351

paper

Sharp Constants of Approximation Theory. III. Certain Polynomial Inequalities of Different Metrics on Convex Sets

arXiv:1902.10215 · doi:10.1016/j.jat.2019.105351

Abstract

Let $V \subset R^{m}$ be a centrally symmetric convex body and let $V^{*} \subset R^{m}$ be its polar. We prove limit relations between the sharp constants in the multivariate Markov-Bernstein-Nikolskii type inequalities for algebraic polynomials on $V^{*}$ and the corresponding constants for entire functions of exponential type with the spectrum in $V$ .

18 pages