Ge´za Freud, orthogonal polynomials and Christoffel functions. A case study
TLDR
In this paper, the authors show that the convergence and absolute convergence of orthogonal polynomials on infinite intervals and on the untt crrcle can be explained by the convergence of Christoffel functions.About:
This article is published in Journal of Approximation Theory.The article was published on 1986-09-01 and is currently open access. It has received 372 citations till now. The article focuses on the topics: Orthogonal polynomials & Discrete orthogonal polynomials.read more
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Orthogonal Polynomials of Several Variables
Charles F. Dunkl,Yuan Xu +1 more
TL;DR: In this article, the authors considered the properties of orthogonal polynomials on the unit sphere, root systems and Coxeter groups, and the Summability of Orthogonal expansions.
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Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
Pavel Bleher,Alexander Its +1 more
TL;DR: In this article, the authors derived semiclassical asymptotics for the orthogonal polynomials Pn(z) on the line with respect to the exponential weight exp(iNV(z)), where V (z) is a double-well quartic polynomial, in the limit when n;N!1.
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The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
TL;DR: In this article, the authors consider polynomials that are orthogonal on [−1,1] with respect to a modified Jacobi weight (1− x ) α (1+ x ) β h (x ), with α, β >−1 and h real analytic and strictly positive on [ −1, 1].
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Multiple orthogonal polynomials
TL;DR: In this paper, a survey of the application of multiple orthogonal polynomials and analytic theory of two model families of general MOPs, referred to as Angelesco and Nikishin systems, is presented.
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Painleve´-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
TL;DR: In this paper, the recurrence coefficients of semi-classical orthogonal polynomials related to a weight function w such that w/w is a rational function were shown to be solutions of nonlinear differential equations with respect to a well-chosen parameter.
References
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Reference BookDOI
Asymptotics and Special Functions
TL;DR: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool as discussed by the authors, and it can be found in many libraries.
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Spectrum estimation and harmonic analysis
TL;DR: In this article, a local eigenexpansion is proposed to estimate the spectrum of a stationary time series from a finite sample of the process, which is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows to treat both bias and smoothing problems.
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Toeplitz Forms and Their Applications.
TL;DR: In this article, Toeplitz forms are used for the trigonometric moment problem and other problems in probability theory, analysis, and statistics, including analytic functions and integral equations.