Weyl-Titchmarsh type formula for Hermite operator with small perturbation
Spectral Theory
2010-03-19 v1
Abstract
Small perturbations of the Jacobi matrix with weights \sqrt n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is analogue of the classical Weyl-Titchmarsh formula for the Schroedinger operator on the half-line with summable potential. Additionally a base of generalized eigenvectors for "free" Hermite operator is studied and asymptotics of Plancherel-Rotach type are obtained.
Cite
@article{arxiv.1003.3596,
title = {Weyl-Titchmarsh type formula for Hermite operator with small perturbation},
author = {Sergey Simonov},
journal= {arXiv preprint arXiv:1003.3596},
year = {2010}
}