Optimal polynomial meshes exist on any multivariate convex domain

TL;DR

This paper proves that optimal polynomial meshes can be constructed for any convex domain in multi-dimensional space, confirming a longstanding conjecture and advancing approximation theory.

Contribution

It establishes the existence of optimal polynomial meshes on all convex bodies in , resolving a conjecture by A. Kroo.

Findings

Optimal polynomial meshes exist for all convex bodies in .

The result confirms a conjecture by A. Kroo.

Provides a foundation for approximation on convex domains.

Abstract

We show that optimal polynomial meshes exist for every convex body in $\mathbb{R}^d$, confirming a conjecture by A. Kroo.