Spectral problems for generalized Jacobi matrices
type: Item
instance of: scholarly article
title: Spectral problems for generalized Jacobi matrices
zbMATH Open document ID: 1053.15018
author: Maxim Derevyagin
author: V. A. Derkach
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: The paper starts by the definition of a new class of generalized Jacobi matrices. Then it shows that every proper rational function is proved to be the \(m-\)function of a unique finite generalized Jacobi matrix. An analog of Stone's theorem that every cyclic self-adjoint operator in a Pontryagin space is unitarily equivalent to some generalized Jacobi matrix is given next. Finally, the convergence of the sequence of subdiagonal \(\left[ L-1/L \right] \) Padé approximants for the corresponding Hamburger series \( \sum\limits_{j=0}^{\infty }\left( -1\right) ^{j}s_{j}z^{j}\) is investigated.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 47B36
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 30B70
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 47A57
zbMATH DE Number: 2081899
zbMATH Keywords: Jacobi matrix
zbMATH Keywords: \(m-\)function
zbMATH Keywords: inverse spectral problem
zbMATH Keywords: Schur algorithm
zbMATH Keywords: continued fraction
zbMATH Keywords: Padé approximant
zbMATH Keywords: Stone's theorem
zbMATH Keywords: Pontryagin space
zbMATH Keywords: convergence
zbMATH Keywords: Hamburger series
reviewed by: Nicholas Karampetakis
MaRDI profile type: Publication
full work available at URL: j.laa.2003.11.003
OpenAlex ID: W1967184917
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DOI: 10.1016/J.LAA.2003.11.003
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description: scientific article; zbMATH DE number 2081899