@Article{Simonov2009,
author = "Simonov, Sergey",
title = "Weyl-Titchmarsh type formula for Hermite operator with small perturbation",
journal = "Opuscula Math.",
year = "2009",
volume = "29",
number = "2",
pages = "187--207",
doi = "http://dx.doi.org/10.7494/OpMath.2009.29.2.187",
url = "http://dx.doi.org/10.7494/OpMath.2009.29.2.187",
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 an analogue of the classical Weyl-Titchmarsh formula for the Schrödinger 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.",
keywords = "Jacobi matrices, absolutely continuous spectrum, subordinacy theory, Weyl-Titchmarsh theory",
issn = "1232-9274"
}