Discrete norming inequalities on sections of sphere, ball and torus

TL;DR

This paper develops discrete trigonometric norming inequalities to create optimal norming meshes for algebraic polynomials on sections of sphere, ball, and torus, improving polynomial approximation techniques on these geometric domains.

Contribution

It introduces a novel approach using discrete trigonometric inequalities to construct norming meshes with optimal growth rates for specific geometric sections.

Findings

Constructed norming meshes with optimal cardinality growth.

Applied inequalities to sections of sphere, ball, and torus.

Enhanced polynomial approximation methods on these domains.

Abstract

By discrete trigonometric norming inequalities on subintervals of the period, we construct norming meshes with optimal cardinality growth for algebraic polynomials on sections of sphere, ball and torus.