Sergey Simonov
Weyl-Titchmarsh type formula for Hermite operator with small perturbation
(364K, pdf)

ABSTRACT.  Small perturbations of the Jacobi matrix with weights n^(1/2) 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 Schrodinger 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.