An estimate for the Green’s function

Research output: Contribution to journalArticle

Abstract

Let K be a continuum on ℂ and let gΩ(K)(z,∞) be the Green’s function of Ω(K) = ℂ¯\K. In a recent paper, V. Totik proved that gΩ(K)(z0,∞) ≤ C dist(z0,∞)1/2 with some non-sharp constant C depending only on the diameter of K. He also used this inequality to prove new results on polynomial approximation in C. In this note we prove a sharp version of Totik’s inequality and discuss a conjectural sharp lower bound for gΩ(K)(z0,∞).

Original languageEnglish
Pages (from-to)3067-3074
Number of pages8
JournalProceedings of the American Mathematical Society
Volume142
Issue number9
DOIs
StatePublished - Sep 1 2014

Keywords

  • Extremal problem
  • Green’s function

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