Titchmarsh-Weyl formula for the spectral density of a class of Jacobi matrices in the critical case

We consider a class of Jacobi matrices with unbounded entries in the so called critical (double root, Jordan box) case. We prove a formula for the spectral density of the matrix which relates its spectral density to the asymptotics of orthogonal polynomials associated with the matrix.

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Bibliographic Details
Main Authors:	Naboko, Serguei, Simonov, Sergey
Format:	Journal Article
Language:	English
Published:	22-11-2019
Subjects:	Mathematics - Mathematical Physics Mathematics - Spectral Theory Physics - Mathematical Physics
Online Access:	Get full text
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Description
Summary:	We consider a class of Jacobi matrices with unbounded entries in the so called critical (double root, Jordan box) case. We prove a formula for the spectral density of the matrix which relates its spectral density to the asymptotics of orthogonal polynomials associated with the matrix.
DOI:	10.48550/arxiv.1911.10282