Smoothness of the Green function for a special domain

Abstract

We consider a compact set K ⊂ ℝ in the form of the union of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions gℂ\K is estimated. Markov's constants of the corresponding set are evaluated. © Instytut Matematyczny PAN, 2012.