A sharp bound on the Lebesgue constant for Leja points in the unit disk

TL;DR

This paper establishes a precise upper bound on the Lebesgue constant for Leja points in the unit disk, confirming a conjecture and advancing understanding of polynomial interpolation stability.

Contribution

It provides the first sharp bound for the Lebesgue constant of Leja sequences in the complex unit disk, resolving a longstanding conjecture.

Findings

Confirmed the conjecture by Calvi and Phung (2011)

Established a sharp bound for the Lebesgue constant

Improved understanding of interpolation stability in complex analysis

Abstract

We give a sharp bound for the Lebesgue constant associated to Leja sequences in the complex unit disk, confirming a conjecture made by Calvi and Phung in 2011