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

Michael I. Ganzburg

Published 2019-02-26Version 1

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 $V$.