Zeros of Faber polynomials for Joukowski airfoils

Autor:	Levenberg, N., Wielonsky, F.
Rok vydání:	2018
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Complex Variables 30C15
Druh dokumentu:	Working Paper
Popis:	Let $K$ be the closure of a bounded region in the complex plane with simply connected complement whose boundary is a piecewise analytic curve with at least one outward cusp. The asymptotics of zeros of Faber polynomials for $K$ are not understood in this general setting. Joukowski airfoils provide a particular class of such sets. We determine the (unique) weak-* limit of the full sequence of normalized counting measures of the Faber polynomials for Joukowski airfoils; it is never equal to the potential-theoretic equilibrium measure of $K$. This implies that many of these airfoils admit an electrostatic skeleton and also explains an interesting class of examples of Ullman related to Chebyshev quadrature. Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1809.10439 Zobrazit plný text záznamu View this record from Arxiv