Strong asymptotics for the continuous Sobolev orthogonal polynomials on the unit circle

DOI10.1006/jath.1999.3358zbMath0934.42017OpenAlexW2024576705MaRDI QIDQ1125471

Elías Berriochoa, Alicia Cachafeiro, Alexander I. Aptekarev

Publication date: 3 April 2000

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.1999.3358

zbMATH Keywords

Sobolev orthogonal polynomialsSobolev inner productSzegö-type functions

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (8)

A necessary condition for the extension of Szegö's asymptotics inside the disk in the Sobolev case ⋮ Sobolev orthogonal polynomials on the unit circle and coherent pairs of measures of the second kind ⋮ Analytic aspects of Sobolev orthogonal polynomials revisited ⋮ Connections between interval and unit circle for Sobolev orthogonal polynomials. Strong asymptotics on the real line ⋮ Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle ⋮ A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: bounds, asymptotics and zeros ⋮ An extension of the coherent pair of measures of the second kind on the unit circle ⋮ Strong asymptotics inside the unit disk for Sobolev orthogonal polynomials.

Cites Work

• Unnamed Item
• Asymptotic properties of Sobolev orthogonal polynomials
• Lebesgue Sobolev orthogonality on the unit circle
• On polynomials orthogonal with respect to Sobolev inner product on the unit circle
• Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials
• Strong asymptotics on the support of the measure of orthogonality for polynomials orthogonal with respect to a discrete Sobolev inner product
• Asymptotics of Sobolev orthogonal polynomials for a Jacobi weight
• Asymptotics of Sobolev orthogonal polynomials for coherent pairs of measures
• Relative asymptotics for orthogonal polynomials with a Sobolev inner product
• Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product
• Extremal polynomials associated with a system of curves in the complex plane
• FUNDAMENTAL PROPERTIES OF POLYNOMIALS ORTHOGONAL ON A CONTOUR

This page was built for publication: Strong asymptotics for the continuous Sobolev orthogonal polynomials on the unit circle