Christoffel functions, Lp Markov inequalities and Marcinkiewicz-Zygmund type discretization for homogeneous polynomials on convex bodies

Kroó, András (2026) Christoffel functions, Lp Markov inequalities and Marcinkiewicz-Zygmund type discretization for homogeneous polynomials on convex bodies. CONSTRUCTIVE APPROXIMATION, 63. pp. 417-446. ISSN 0176-4276

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Abstract

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 Lp 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

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