Cesàro asymptotics for orthogonal polynomials on the unit circle and classes of measures

DOI10.1006/jath.2001.3655zbMath1007.42018OpenAlexW2062753932MaRDI QIDQ696864

Sergei Khrushchev, Leonid B. Golinskii

Publication date: 12 September 2002

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

Full work available at URL: https://semanticscholar.org/paper/c4874a9ea599c20aedb8a4e68dfc18d4345c8799

zbMATH Keywords

orthogonal polynomialsCesàro summabilityreflection coefficientsNevai classSchur functionSzegő classRakhmanov classWall continued fraction

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Continued fractions; complex-analytic aspects (30B70) Convergence and divergence of continued fractions (40A15)

Related Items (7)

Analogs of the \(m\)-function in the theory of orthogonal polynomials on the unit circle ⋮ Classification theorems for general orthogonal polynomials on the unit circle ⋮ Asymptotics of the \(L^2\) norm of derivatives of OPUC ⋮ Weak convergence of CD kernels and applications ⋮ Regularity and the Cesàro-Nevai class ⋮ Turán measures ⋮ Orthogonal rational functions with real poles, root asymptotics, and GMP matrices

Cites Work

• Classification theorems for general orthogonal polynomials on the unit circle
• Extensions of Szegö's theory of orthogonal polynomials. II
• On some classes of polynomials orthogonal on arcs of the unit circle connected with symmetric orthogonal polynomials on an interval
• Quadrature formula and zeros of para-orthogonal polynomials on the unit circle
• Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle
• Perturbation of orthogonal polynomials on an arc of the unit circle
• A special class of polynomials orthogonal on the unit circle including the associated polynomials
• Singular measures on the unit circle and their reflection coefficients
• Continuation methods for the computation of zeros of Szegő polynomials
• ON THE ASYMPTOTICS OF THE RATIO OF ORTHOGONAL POLYNOMIALS. II
• Strong and Weak Convergence of Orthogonal Polynomials
• ON THE ASYMPTOTICS OF THE RATIO OF ORTHOGONAL POLYNOMIALS
• Continued fractions and bounded analytic functions
• Schur's algorithm, orthogonal polynomials, and convergence of Wall's continued fractions in \(L^2(\mathbb{T})\).
• A singular Riesz product in the Nevai class and inner functions with the Schur parameters in \(\cap_{p>2}I^p\)
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