Orthogonal polynomials on the circumference and arcs of the circumference

DOI10.1006/jath.1999.3383zbMath0956.42017OpenAlexW1973324107MaRDI QIDQ1969972

Franz Peherstorfer, Robert Steinbauer

Publication date: 21 February 2001

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

Full work available at URL: https://doi.org/10.1006/jath.1999.3383

zbMATH Keywords

reflection coefficientsorthogonal polynomials on the unit circleseveral arcs

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Other special orthogonal polynomials and functions (33C47)

Related Items (9)

On higher-order Szegő theorems with a single critical point of arbitrary order ⋮ Mass points of measures and orthogonal polynomials on the unit circle ⋮ Orthogonal polynomials with recursion coefficients of generalized bounded variation ⋮ OPUC on one foot ⋮ Zeros of polynomials orthogonal on two arcs of the unit circle ⋮ Asymptotics of orthogonal polynomials and point perturbation on the unit circle ⋮ Generalized Prüfer variables for perturbations of Jacobi and CMV matrices ⋮ Applications of a new formula for OPUC with periodic Verblunsky coefficients ⋮ Probability measures with reflection coefficients \(\{a_n\} \in \ell^4\) and \(\{a_{n+1}-a_n\} \in \ell^2\) are Erdős measures

Cites Work

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• Ratio asymptotics for polynomials orthogonal on arcs on the unit circle
• Asymptotic behaviour of orthogonal polynomials on the unit circle with asymptotically periodic reflection coefficients
• Ratio and relative asymptotics of polynomials orthogonal on an arc of the unit circle
• Perturbation of orthogonal polynomials on an arc of the unit circle
• Extremal polynomials associated with a system of curves in the complex plane
• Orthogonal polynomials on arcs of the unit circle. II: Orthogonal polynomials with periodic reflection coefficients
• ASYMPTOTIC PROPERTIES OF POLYNOMIALS ORTHOGONAL ON A SYSTEM OF CONTOURS, AND PERIODIC MOTIONS OF TODA LATTICES
• Strong Asymptotics of Orthonormal Polynomials with the Aid of Green's Function
• Comparative asymptotics for perturbed orthogonal polynomials

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