Analytic Scattering Theory for Jacobi Operators and Bernstein-Szego Asymptotics of Orthogonal Polynomials

被引：5

作者：

Yafaev, D. R. ^{[1
,2
]}

机构：

[1] Univ Rennes 1, IRMAR, Campus Beaulieu, F-35042 Rennes, France

[2] SPGU, Univ Nab 7-9, St Petersburg 199034, Russia

来源：

REVIEWS IN MATHEMATICAL PHYSICS | 2018年 / 30卷 / 08期

基金：

俄罗斯科学基金会;

关键词：

Jacobi matrices; discrete Schrodinger operator; orthogonal polynomials; asymptotics for large numbers; Szego function; MATRICES;

D O I：

10.1142/S0129055X18400196

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study semi-infinite Jacobi matrices H = H-0 + V corresponding to trace class perturbations V of the "free" discrete Schrodinger operator H-0. Our goal is to construct various spectral quantities of the operator H, such as the weight function, eigenfunctions of its continuous spectrum, the wave operators for the pair H-0, H, the scattering matrix, the spectral shift function, etc. This allows us to find the asymptotic behavior of the orthonormal polynomials P-n(z) associated to the Jacobi matrix H as n -> infinity. In particular, we consider the case of z inside the spectrum [-1, 1] of H-0 when this asymptotic has an oscillating character of the Bernstein-Szego type and the case of z at the end points +/- 1.

引用

页数：47