Multipoint Schur algorithm and orthogonal rational functions. I: Convergence properties

DOI10.1007/s11854-011-0016-9zbMath1248.30015arXiv0812.2050OpenAlexW2078704822MaRDI QIDQ415769

J. Herrera, H. S. Yoon

Publication date: 9 May 2012

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.2050

zbMATH Keywords

orthogonal rational functionsSchur algorithmmultipoint Schur approximantsSzegő theoryWall rational functions

Mathematics Subject Classification ID

Continued fractions; complex-analytic aspects (30B70) Other special orthogonal polynomials and functions (33C47) Blaschke products (30J10)

Related Items

The Jacobi matrices approach to Nevanlinna-Pick problems ⋮ Baxter's difference systems and orthogonal rational functions ⋮ Schur's criterion for formal Newton series ⋮ Necessary and sufficient conditions for extending a function to a Schur function ⋮ The linear pencil approach to rational interpolation ⋮ How poles of orthogonal rational functions affect their Christoffel functions ⋮ Periodic GMP matrices ⋮ Jacobi flow on SMP matrices and Killip-Simon problem on two disjoint intervals

Cites Work

• The absolutely continuous spectrum of Jacobi matrices
• Classification theorems for general orthogonal polynomials on the unit circle
• An expansion for polynomials orthogonal over an analytic Jordan curve
• Wall rational functions and Khrushchev's formula for orthogonal rational functions
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• Sum rules for Jacobi matrices and their applications to spectral theory
• Solution of a multiple Nevanlinna--Pick problem via orthogonal rational functions
• Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight
• The Riemann--Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
• Orthogonal polynomials and a generalized Szegő condition
• Asymptotics of the orthogonal polynomials for the Szegő class with a polynomial weight
• Zero distributions via orthogonality.
• Convergent interpolation to Cauchy integrals over analytic arcs
• Asymptotics of orthonormal polynomials in the presence of a denumerable set of mass points
• Asymptotics of orthogonal polynomials with respect to an analytic weight with algebraic singularities on the circle
• The Steepest Descent Method for Orthogonal Polynomials on the Real Line with Varying Weights
• Weakly Differentiable Functions
• Sharp constants for rational approximations of analytic functions
• Continued fractions and bounded analytic functions
• Schur's algorithm, orthogonal polynomials, and convergence of Wall's continued fractions in \(L^2(\mathbb{T})\).
• On the convergence of rational functions orthogonal on the unit circle
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