Directional Chebyshev Constants on the Boundary

TL;DR

This paper establishes the existence of limits for weighted directional Chebyshev constants at all points on the standard simplex for regular compact sets in complex d-dimensional space, advancing potential theory.

Contribution

It proves the existence of limits of weighted directional Chebyshev constants at all points of the standard simplex for regular compact sets in complex space.

Findings

Limits of weighted directional Chebyshev constants exist at all points of the standard simplex.

Results apply to (locally) regular compact sets in complex space.

Advances potential theory related to Chebyshev constants.

Abstract

We prove results on existence of limits in the definition of (weighted) directional Chebyshev constants at all points of the standard simplex $\Sigma \subset {\bf R}^d$ for (locally) regular compact sets $K\subset {\bf C}^d$.