an:06004439
Zbl 1236.42021
Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
Finite gap Jacobi matrices. II: The Szegő class
EN
Constr. Approx. 33, No. 3, 365-403 (2011).
0176-4276 1432-0940
2011
j
42C05 58J53 14H30 47B36
isospectral torus; Szegő asymptotics; orthogonal polynomials
The authors study Jacobi matrices \(J\) and asymptotics of the associated orthogonal polynomials, where \(\sigma_{\text{ess}}(J)\) is a finite union of disjoint closed intervals. They study Szegő's theorem for the general finite gap case. They use Remling's theorem about the approach to the isospectral torus together with an analysis of Jost functions to provide a new proof of Szegő asymptotics including \(L^{2}\) Szegő asymptotics on the spectrum.
For Part I, see ibid. 32, No.~1, 1--65 (2010; Zbl 1200.42012).
Chrysoula G. Kokologiannaki (Patras)
1200.42012