Upper estimates of Christoffel function on convex domains

Abstract

New upper bounds on the pointwise behaviour of Christoffel function on convex domains in ${\mathbb{R}}^d$ are obtained. These estimates are established by explicitly constructing the corresponding "needle"-like algebraic polynomials having small integral norm on the domain, and are stated in terms of few easy-to-measure geometric characteristics of the location of the point of interest in the domain. Sharpness of the results is shown and examples of applications are given.

References in corpus (1)

• On Nikol'skii inequalities for domains in $R^d$

Cited by in corpus (3)

• Geometric computation of Christoffel functions on planar convex domains
• Approximation and localized polynomial frame on conic domains
• Christoffel function on planar domains with piecewise smooth boundary