An analog of the trace formula for discrete Sturm-Liouville operators with asymptotically \(n\)-periodic coefficients
type: Item
instance of: scholarly article
title: An analog of the trace formula for discrete Sturm-Liouville operators with asymptotically \(n\)-periodic coefficients
zbMATH Open document ID: 0927.47025
DOI: 10.1007/BF02466063
publication date: 1999-12-13T00:00:00Z
review text: Let Nevai's class \(M\) of Jacobi matrices \[ J= \left[\begin{matrix} b_0 & a_1 & 0 & 0 &\cdot &\cdot &\cdot &\cdot\\ a_1 & b_1 & a_2 & 0 &\cdot &\cdot &\cdot &\cdot\\ 0 & a_2 & b_2 & a_3 &\cdot &\cdot &\cdot &\cdot\\ \cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot\\ \cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot\\ \cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot\end{matrix}\right]\text{ such that }\underset{n\to\infty} {\text{lim}} a_n= 1/2,\text{ and }\underset{n\to \infty} {\text{lim}} b_n=0. \] In this paper, a connection between the Jacobi matrix \(J\) from the class \(M\) and the corresponding spectral measure is established.
reviewed by: B. M. Agrawal
Mathematics Subject Classification ID: 47B39
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 39A70
zbMATH DE Number: 1226011
zbMATH Keywords: Nevai's class
zbMATH Keywords: Jacobi matrices
zbMATH Keywords: spectral measure
author: B. P. Osilenker
MaRDI profile type: Publication
cites work: Q3994435
cites work: Orthogonal Polynomials, Measures and Recurrence Relations
cites work: Orthogonal polynomials with asymptotically periodic recurrent coefficients
cites work: On Sieved Orthogonal Polynomials I: Symmetric Pollaczek Analogues
cites work: On Sieved Orthogonal Polynomials. V: Sieved Pollaczek Polynomials
cites work: Approximating the weight function for orthogonal polynomials on several intervals
full work available at URL: https://doi.org/10.1007/bf02466063
OpenAlex ID: W2081213364
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1226011