Asymptotic behaviour of orthogonal polynomials on the unit circle with asymptotically periodic reflection coefficients

DOI10.1006/jath.1996.3026zbMath0889.42021OpenAlexW2013796135MaRDI QIDQ1354683

Robert Steinbauer, Franz Peherstorfer

Publication date: 1 June 1998

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

Full work available at URL: https://doi.org/10.1006/jath.1996.3026

zbMATH Keywords

reflection coefficientsasymptotic periodicityorthogonal polynomials on the unit circle

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Polynomials and rational functions of one complex variable (30C10)

Related Items

Discrete spectrum of the Jacobi matrix related to recurrence relations with periodic coefficients, Verblunsky coefficients related with periodic real sequences and associated measures on the unit circle, Asymptotic behavior of solutions of general three term recurrence relations, Ratio and relative asymptotics of polynomials orthogonal on an arc of the unit circle, On the zeros of orthogonal polynomials on the unit circle, Orthogonal polynomials on the circumference and arcs of the circumference, OPUC on one foot, Orthogonal and \(L_q\)-extremal polynomials on inverse images of polynomial mappings, Classification theorems for general orthogonal polynomials on the unit circle, Zeros of polynomials orthogonal on two arcs of the unit circle, Akhiezer's orthogonal polynomials and Bernstein-Szegő method for a circular arc, Perturbation of orthogonal polynomials on an arc of the unit circle. II, Applications of a new formula for OPUC with periodic Verblunsky coefficients, Asymptotic behaviour of orthogonal polynomials on the unit circle with asymptotically periodic reflection coefficients. II: Weak asymptotics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Orthogonal polynomials with asymptotically periodic recurrent coefficients
• Szegö's extremum problem on the unit circle
• On the asymptotic behaviour of functions of the second kind and Stieltjes polynomials and on the Gauss-Kronrod quadrature formulas
• Perturbation of orthogonal polynomials on an arc of the unit circle
• Orthogonal polynomials on arcs of the unit circle. I
• A special class of polynomials orthogonal on the unit circle including the associated polynomials
• Orthogonal polynomials on arcs of the unit circle. II: Orthogonal polynomials with periodic reflection coefficients
• On the distribution of zeros of polynomials orthogonal on the unit circle
• On Bernstein-Szegö orthogonal polynomials on several intervals. II: Orthogonal polynomials with periodic recurrence coefficients
• Comparative asymptotics for perturbed orthogonal polynomials