2011/07/29 by Carmen Escribano, Escribano, Carmen, Antonio Giraldo +7
Mathematics · #Advanced Algebra and Geometry #Analytic and geometric function theory #Holomorphic and Operator Theory #math.CV #math.FA #math.SP
paper · pdf · doi:10.48550/arxiv.1107.6036
arxiv created 2011/11/06 · arxiv updated 2011/11/08
We consider a Jordan arc Γin the complex plane ℂ and a regular measure μwhose support is Γ. We denote by D the upper Hessenberg matrix of the multiplication by z operator with respect to the orthonormal polynomial basis associated with μ. We show in this work that, if the Hessenberg matrix D is uniformly asymptotically Toeplitz, then the symbol of the limit operator is the restriction to the unit circle of the Riemann mapping function ϕ(z) which maps conformally the exterior of the unit disk onto the exterior of the support of the measure μ. We use this result to show how to approximate the Riemann mapping function for the support of μfrom the entries of the Hessenberg matrix D.