Jost Functions and Jost Solutions for Jacobi Matrices, I. A Necessary and Sufficient Condition for Szego Asymptotics
David Damanik, Barry Simon
Abstract
We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szegő asymptotics off the real axis. A key idea is to prove the equivalence of Szegő asymptotics and of Jost asymptotics for the Jost solution. We also prove L2 convergence of Szegő asymptotics on the spectrum.
Create a lesson
Related papers
Sharp upper bounds for Steklov eigenvalues on warped products
Jade Brisson, Bruno Colbois, Alexandre Girouard et al.
Non-Bloch band theory for finite banded non-Hermitian Toeplitz matrices
Yannick de Bruijn, Erik Orvehed Hiltunen
Non-resonant angles in a Robin eigenvalue problem
Konstantin Pankrashkin
Sums of Dirichlet eigenvalues in proximity of the disk and the ball
Matthias Baur
On the inequality μ3 < λ1 for the eigenvalues of the Laplace operator
N. Filonov
Quantitative spectral stability and sharp Fourier estimates for periodic CMV matrices with decaying perturbations
Moacir Aloisio, César R. de Oliveira, Mariane Pigossi