Weyl-Titchmarsh type formula for Hermite operator with small perturbation

Details Weyl-Titchmarsh type formula for Hermite operator with small perturbation Weyl-Titchmarsh type formula for Hermite operator with small perturbation

2010-03-18

arxiv.org/abs/1003.3596v1

Opuscula Mathematica, volume 29(2), pages 187-207, 2009

Mathematics

Spectral Theory

Scientific paper

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.

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