Absolute continuity for unbounded Jacobi matrices with constant row sums
type: Item
instance of: scholarly article
title: Absolute continuity for unbounded Jacobi matrices with constant row sums
zbMATH Open document ID: 1030.42020
author: Joanne Dombrowski
author: Steen Pedersen
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-11-04T00:00:00Z
review text: In the present paper the authors study two classes of Jacobi matrices. The first one consists of the matrices with zero diagonal \((b_n=0)\) and the off diagonal sequences \(a_n\) which satisfy \[ a_{2n-1}=a_{2n}=n+\varepsilon, \qquad \varepsilon\geq 0, \quad n\geq 1. \] The authors show that the spectral measures of such matrices are absolutely continuous. The second class includes generic Jacobi matrices with \[ a_n=(n+\varepsilon_n)^2, \qquad a_{n-1}+b_n+a_n=0. \] The corresponding spectral measures are proved to have an absolutely continuous part as long as \(\varepsilon_n\) is of bounded variation and \(\varepsilon_n \geq 0\).
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 47B36
zbMATH DE Number: 1749679
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: weighted shift
zbMATH Keywords: absolute continuity
zbMATH Keywords: Jacobi matrices
reviewed by: Leonid Golinskii
MaRDI profile type: Publication
full work available at URL: jmaa.2001.7808
OpenAlex ID: W2015591676
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DOI: 10.1006/JMAA.2001.7808
description: scientific article; zbMATH DE number 1749679