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<p>In this paper we will study various extremal problems related to multivariate homogeneous polynomials on convex bodies. We will construct certain homogeneous needle polynomials on convex bodies which will play a central role in the study of the asymptotics of Christoffel functions and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> Markov type estimates for homogeneous polynomials. These new results will be applied in order to derive asymptotically optimal Marcinkiewicz-Zygmund type meshes and cubature formulas for homogeneous polynomials on convex bodies</p>

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Christoffel functions, \(L^p\) Markov inequalities and Marcinkiewicz-Zygmund type discretization for homogeneous polynomials on convex bodies

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  • 发表日期：

    2025年11月13日

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  • András Kroó

摘要

In this paper we will study various extremal problems related to multivariate homogeneous polynomials on convex bodies. We will construct certain homogeneous needle polynomials on convex bodies which will play a central role in the study of the asymptotics of Christoffel functions and \(L^p\) L p Markov type estimates for homogeneous polynomials. These new results will be applied in order to derive asymptotically optimal Marcinkiewicz-Zygmund type meshes and cubature formulas for homogeneous polynomials on convex bodies