TY  - JOUR
ID  - Simonov2009
LB  - Simonov2009
AU  - Simonov, Sergey
TI  - Weyl-Titchmarsh type formula for Hermite operator with small perturbation
ST  - Weyl-Titchmarsh type formula for Hermite operator with small perturbation
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2009
VL  - 29
IS  - 2
SP  - 187
EP  - 207
DO  - http://dx.doi.org/10.7494/OpMath.2009.29.2.187
UR  - http://dx.doi.org/10.7494/OpMath.2009.29.2.187
AB  - 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.
KW  - Jacobi matrices
KW  - absolutely continuous spectrum
KW  - subordinacy theory
KW  - Weyl-Titchmarsh theory
SN  - 1232-9274
ER  -