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 SchrÃ¶dinger 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 -