Weyl-titchmarsh Type Formula for Hermite Operator with Small Perturbation
نویسنده
چکیده
Small perturbations of the Jacobi matrix with weights √ 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 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.
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تاریخ انتشار 2008