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arXiv · 2007.08439

Sharp Constants of Approximation Theory. V. An Asymptotic Equality Related to Polynomials with Given Newton Polyhedra

Michael Ganzburg
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Abstract

Let $V\subset\R^m$ be a convex body, symmetric about all coordinate hyperplanes, and let $\PP_{aV},\, a\ge 0$, be a set of all algebraic polynomials whose Newton polyhedra are subsets of $aV$. We prove a limit equality as $a\to \iy$ between the sharp constant in the multivariate Markov-Bernstein-Nikolskii type inequalities for polynomials from $\PP_{aV}$ and the corresponding constant for entire functions of exponential type with the spectrum in $V$.

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Michael Ganzburg. 2020-07-16. Sharp Constants of Approximation Theory. V. An Asymptotic Equality Related to Polynomials with Given Newton Polyhedra. https://arxiv.org/abs/2007.08439

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