Weyl-Titchmarsh type formula for Hermite operator with small perturbation

• Autorzy: Simonov S.
• Języki publikacji: EN

Abstrakty

EN

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 an analogue of the classical Weyl-Titchmarsh formula for the Schr ödinger 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.

Słowa kluczowe

EN

Jacobi matrices; absolutely continuous spectrum; subordinacy theory; Weyl-Titchmarsh theory

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2009
• Tom: Vol. 29, no. 2
• Strony: 187--207
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Simonov S.

• Institute of Physics, St. Petersburg University, Department of Mathematical Physics Ulianovskaia 1, 198904, St. Petergoff, St. Petersburg, Russia,

Bibliografia

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