Orthogonal polynomials on the unit circle: distribution of zeros

DOI10.1016/0377-0427(91)90118-4zbMath0745.42013OpenAlexW2077501145MaRDI QIDQ1184791

Eduardo Paciência Godoy, Francisco Marcellán

Publication date: 28 June 1992

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(91)90118-4

zbMATH Keywords

quadrature formulaToeplitz matricesHessenberg matrixGohberg-Semencul formulazeros of orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Nonlinear algebraic or transcendental equations (65H99)

Related Items (8)

On zeros of polynomials orthogonal with respect to a quasi-definite inner product on the unit circle ⋮ Orthogonal Laurent polynomials on the unit circle, extended CMV ordering and 2D Toda type integrable hierarchies ⋮ Matrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systems ⋮ On Szegő's theorem for a nonclassical case ⋮ A matrix approach to the computation of quadrature formulas on the unit circle ⋮ OPUC, CMV matrices and perturbations of measures supported on the unit circle ⋮ Minimal representations of unitary operators and orthogonal polynomials on the unit circle ⋮ Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle

Cites Work

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• On two theorems of M. G. Krein concerning polynomials orthogonal on the unit circle
• On some open problems of approximation theory
• Downdating of Szegö polynomials and data-fitting applications
• A class of orthogonal polynomials
• On some problems connected with polynomials orthogonal on the complex unit circle
• ON THE ASYMPTOTICS OF THE RATIO OF ORTHOGONAL POLYNOMIALS. II
• Computing the Roots of Complex Orthogonal and Kernel Polynomials
• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle
• \Delta -Coherent Pairs and Orthogonal Polynomials of a Discrete Variable
• Maximum entropy and the moment problem

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