Christoffel functions, $$L^p$$ Markov inequalities and Marcinkiewicz-Zygmund type discretization for homogeneous polynomials on convex bodies
Year: 2025
Type: article
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 $$L^p$$ 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
Source: Constructive Approximation
Author: András Kroó
Institution: HUN-REN Alfréd Rényi Institute of Mathematics
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4416178391