Asymptotics of the \(L^2\) norm of derivatives of OPUC

DOI10.1016/j.jat.2010.09.002zbMath1220.42019arXiv1006.0900OpenAlexW2084322070MaRDI QIDQ547879

Barry Simon, Andrei Martínez-Finkelshtein

Publication date: 27 June 2011

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

Full work available at URL: https://arxiv.org/abs/1006.0900

zbMATH Keywords

orthogonal polynomialsnormal derivativesVerblunsky coefficientsderivative asymptoticsSzegő condition

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10)

Related Items

Para-orthogonal polynomials on the unit circle satisfying three term recurrence formulas, On computational aspects of discrete Sobolev inner products on the unit circle, Asymptotic behaviour of Sobolev orthogonal polynomials on the unit circle, On Some Recent Results on Asymptotic Behavior of Orthogonal Polynomials on the Unit Circle and Inserting Point Masses

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cesàro asymptotics for orthogonal polynomials on the unit circle and classes of measures
• Behavior of best \(L_ p\) polynomial approximants on the unit interval and on the unit circle
• Asymptotics of derivatives of orthogonal polynomials on the unit circle
• A fast algorithm for proving terminating hypergeometric identities
• Weak convergence of CD kernels and applications
• Extensions of Szegö's theory of orthogonal polynomials. III
• The method of creative telescoping
• The asymptotic representation at a point of the derivative of orthonormal polynomials
• Asymptotic properties of balanced extremal Sobolev polynomials: Coherent case
• A \textit{Mathematica} version of Zeilberger's algorithm for proving binomial coefficient identities
• Uniform asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights
• Equilibrium measures and capacities in spectral theory
• A class of orthogonal polynomials
• An Asymptotic Formula for the Derivatives of Orthogonal Polynomials
• Asymptotics of orthogonal polynomials with respect to an analytic weight with algebraic singularities on the circle
• The Formula steepest descent method and the asymptotic behavior of polynomials orthogonal on the unit circle with fixed and exponentially varying nonanalytic weights
• Sobolev orthogonal polynomials: Balance and asymptotics
• THE ASYMPTOTIC BEHAVIOR OF ORTHOGONAL POLYNOMIALS
• Gap probabilities in the finite and scaled Cauchy random matrix ensembles
• Pointwise estimates from below of the moduli of the derivatives of orthogonal polynomials on the circle with a weight having singularities
• The Christoffel-Darboux Kernel
• An Asymptotic Formula for the Derivatives of Orthogonal Polynomials of the Unit Circle.
• The Nevai condition