Opuscula Mathematica
Opuscula Math. 29, no. 2 (), 187-207
Opuscula Mathematica

Weyl-Titchmarsh type formula for Hermite operator with small perturbation

Abstract. 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.
Keywords: Jacobi matrices, absolutely continuous spectrum, subordinacy theory, Weyl-Titchmarsh theory.
Mathematics Subject Classification: 47A10, 47B36.
Cite this article as:
Sergey Simonov, Weyl-Titchmarsh type formula for Hermite operator with small perturbation, Opuscula Math. 29, no. 2 (2009), 187-207, http://dx.doi.org/10.7494/OpMath.2009.29.2.187
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.