scholarly journals Analytic Scattering Theory for Jacobi Operators and Bernstein–Szegö Asymptotics of Orthogonal Polynomials

2018 ◽  
pp. 567-613
Author(s):  
D. R. Yafaev
Keyword(s):  
Orthogonal Polynomials ◽  
Scattering Theory ◽  
Jacobi Operators ◽  
Asymptotics Of Orthogonal Polynomials ◽  
Szego Asymptotics

scholarly journals Analytic Scattering Theory for Jacobi Operators and Bernstein–Szegö Asymptotics of Orthogonal Polynomials

2018 ◽  
Vol 30 (08) ◽  
pp. 1840019 ◽  
Author(s):  
D. R. Yafaev
Keyword(s):  
Jacobi Matrix ◽  
Trace Class ◽  
Spectral Shift ◽  
Shift Function ◽  
Discrete Schrödinger Operator ◽  
Wave Operators ◽  
Jacobi Operators ◽  
Matrix Formula ◽  
Asymptotics Of Orthogonal Polynomials ◽  
Szego Asymptotics

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].

scholarly journals Scattering Theory for Jacobi Operators with Quasi-Periodic Background

2006 ◽  
Vol 264 (3) ◽  
pp. 811-842 ◽  
Author(s):  
Iryna Egorova ◽  
Johanna Michor ◽  
Gerald Teschl
Keyword(s):  
Scattering Theory ◽  
Jacobi Operators
Sign in / Sign up

Export Citation Format

Share Document