127 research outputs found
Weyl-Titchmarsh type formula for Hermite operator with small perturbation
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
Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case
We consider a class of Jacobi matrices with periodically modulated diagonal
in a critical hyperbolic ("double root") situation. For the model with
"non-smooth" matrix entries we obtain the asymptotics of generalized
eigenvectors and analyze the spectrum. In addition, we reformulate a very
helpful theorem from a paper of Janas and Moszynski in its full generality in
order to serve the needs of our method
Spectral multiplicity of selfadjoint Schrodinger operators on star-graphs with standard interface conditions
We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schroedinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the interior vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of Theorem of I.S. Kac
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