asymptotics of orthogonal polynomials
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2019 ◽  
Vol 144 (2) ◽  
pp. 133-163
Author(s):  
Wen‐Gao Long ◽  
Dan Dai ◽  
Yu‐Tian Li ◽  
Xiang‐Sheng Wang


2018 ◽  
Vol 30 (08) ◽  
pp. 1840019 ◽  
Author(s):  
D. R. Yafaev

We study semi-infinite Jacobi matrices [Formula: see text] corresponding to trace class perturbations [Formula: see text] of the “free” discrete Schrödinger operator [Formula: see text]. Our goal is to construct various spectral quantities of the operator [Formula: see text], such as the weight function, eigenfunctions of its continuous spectrum, the wave operators for the pair [Formula: see text], [Formula: see text], the scattering matrix, the spectral shift function, etc. This allows us to find the asymptotic behavior of the orthonormal polynomials [Formula: see text] associated to the Jacobi matrix [Formula: see text] as [Formula: see text]. In particular, we consider the case of [Formula: see text] inside the spectrum [Formula: see text] of [Formula: see text] when this asymptotic has an oscillating character of the Bernstein–Szegö type and the case of [Formula: see text] at the end points [Formula: see text].





2018 ◽  
Vol 209 (3) ◽  
pp. 449-468
Author(s):  
E. B. Saff ◽  
N. Stylianopoulos






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