On Lebesgue Constants for Interpolation Points on a Quasiconformal Arc
Vladimir Andrievskii
TL;DR
This paper simplifies the proof of how Lebesgue constants behave for interpolation points on a quasiconformal arc using quasiconformal mapping theory, advancing understanding in complex approximation theory.
Contribution
It provides a simplified proof of a recent result on Lebesgue constants for interpolation points on quasiconformal arcs, utilizing quasiconformal mapping theory.
Findings
Simplified proof of Lebesgue constant behavior
Application of quasiconformal mappings in approximation theory
Enhanced understanding of interpolation on complex sets
Abstract
Using the theory of quasiconformal mappings, we simplify the proof of the recent result by Taylor and Totik (see IMA Journal of Numerical Analysis 30 (2010) 462--486) on the behavior of the Lebesgue constants for interpolation points on a compact set in the complex plane.
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