On semi-classical weight functions on the unit circle

IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2023-08-16 DOI:10.1016/j.jat.2023.105957

Cleonice F. Bracciali , Karina S. Rampazzi , Luana L. Silva Ribeiro

引用次数: 0

Abstract

We consider orthogonal polynomials on the unit circle associated with certain semi-classical weight functions. This means that the Pearson-type differential equations satisfied by these weight functions involve two polynomials of degree at most 2. We determine all such semi-classical weight functions and this also includes an extension of the Jacobi weight function on the unit circle. General structure relations for the orthogonal polynomials and non-linear difference equations for the associated complex Verblunsky coefficients are established. As application, we present several new structure relations and non-linear difference equations associated with some of these semi-classical weight functions.

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单位圆上的半经典权函数

我们考虑与某些半经典权函数相关的单位圆上的正交多项式。这意味着这些权函数所满足的皮尔逊型微分方程包含两个至多2次的多项式。我们确定了所有这样的半经典权函数，这也包括Jacobi权函数在单位圆上的扩展。建立了正交多项式的一般结构关系和相关复Verblunsky系数的非线性差分方程。作为应用，我们提出了几个新的结构关系和与这些半经典权函数相关的非线性差分方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.

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