Asymptotic properties of extremal polynomials corresponding to measures supported on analytic regions (Q387376)

Let \(G\) be a bounded region with simply connected closure and analytic boundary and let \(\mu\) be a positive measure supported by the closure of \(G\) together with finitely many pure points outside \(G\). The study presented here is motivated by a paper [\textit{F. Nazarov} et al., Math. Res. Lett. 13, No. 5--6, 975--983 (2006; Zbl 1110.41015)] who showed that the appropriate analogue of Szegő's theorem (cf. Theorem 7.1 in [\textit{Ja. L. Geronimus}, Mat. Sb., Nov. Ser. 31(73), 3--26 (1952; Zbl 0049.08502)]) holds when \(\mu\) can be written as the sum of a measure supported by \(\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}\), a Szegő measure on \(\delta \mathbb{D}\) with no singular part, and a pure point measure carried by the compliment of closure of \(\mathbb{D}\). The authors provide leading order asymptotics for the monic orthogonal polynomial norms in a related setting. They also cite a paper by \textit{T. Bloom} et al. [``New perspectives in univariate and multivariate orthogonal polynomials'', Report from Banff International Research Station, October (2010)], for a somewhat similar study.