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Article Dans Une Revue Reviews in Mathematical Physics Année : 2018

ANALYTIC SCATTERING THEORY FOR JACOBI OPERATORS AND BERNSTEIN-SZEGO ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS

Résumé

We study semi-infinite Jacobi matrices H = H 0 + V corresponding to trace class perturbations V of the " free " discrete Schrödinger 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 → ∞. In particular, we consider the case of z inside the spectrum [−1, 1] of H 0 when this asymptotics has an oscillating character of the Bernstein-Szegö type and the case of z at the end points ±1.
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Dates et versions

hal-01673042 , version 1 (28-12-2017)

Identifiants

Citer

Dimitri R Yafaev. ANALYTIC SCATTERING THEORY FOR JACOBI OPERATORS AND BERNSTEIN-SZEGO ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS. Reviews in Mathematical Physics, 2018, 30 (8), pp.1840019. ⟨10.1142/S0129055X18400196⟩. ⟨hal-01673042⟩
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