Lectures on complex approximation
Lectures on complex approximation
Perturbation of orthogonal polynomials on an arc of the unit circle
Journal of Approximation Theory
Ratio and relative asymptotics of polynomials orthogonal on an arc of the unit circle
Journal of Approximation Theory
Spectral Properties of Banded Toeplitz Matrices
Spectral Properties of Banded Toeplitz Matrices
Rakhmanov's theorem for orthogonal matrix polynomials on the unit circle
Journal of Approximation Theory
Computing the Hessenberg matrix associated with a self-similar measure
Journal of Approximation Theory
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We consider a Jordan arc Γ in the complex plane ${\mathbb C}$ and a regular measure μ whose 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 驴(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 μ from the entries of the Hessenberg matrix D.