Bernstein-Szegö asymptotique des polynômes orthogonaux

We study semi-infinite Jacobi matrices $H=H_{0}+V$ corresponding to trace class perturbations $V$ of the "free" discrete Schrödinger operator $H_{0}$ and properties of the associated orthonormal polynomials $P_{n}(z)$. 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   polynomials $P_{n}(z)$ as $n\to\infty$ and gives a new look on the Bernstein-Szegö formulas. We give a proof of these formulas under essentially more general circumstances than in the original papers.