Characteristics of spectra of higher order difference operators and the convergence of the joint rational approximations
type: Item
instance of: scholarly article
title: Characteristics of spectra of higher order difference operators and the convergence of the joint rational approximations
zbMATH Open document ID: 0927.47024
published in: Doklady Mathematics
publication date: 1999-12-13T00:00:00Z
review text: The issue concerning the relations between joint Hermite-Pade approximations and polynomials determined by orthogonal relations systems on one hand, and operator spectral theory on the other hand, has been open for a long time. In this article, we present results obtained in that direction. It has been found that the convergence of joint approximations is connected with the characteristics of the spectrum of some difference operator of \(p+1\) order, which, in an appropriate basis, can be represented in the form of an essentially asymmetric \((p+2)\)-diagonal matrix. In our presentation of the results we constrain ourselves to the case \(p=2\), and separately note the modifications needed for the case \(p>2\).
Mathematics Subject Classification ID: 47B39
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 47N40
zbMATH DE Number: 1050660
zbMATH Keywords: Hermite-Pade approximations
zbMATH Keywords: operator spectral theory
zbMATH Keywords: spectrum of some difference operator
author: Valery A. Kalyagin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1050660