A generalization of the one-step theorem for matrix polynomials
type: Item
instance of: scholarly article
title: A generalization of the one-step theorem for matrix polynomials
zbMATH Open document ID: 1036.30005
author: I. Gohberg
author: Robert L. Ellis
published in: Integral Equations and Operator Theory
publication date: 2004-01-05T00:00:00Z
review text: The authors give a new proof of Krein's theorem for orthogonal matrix polynomials based on a ``one-step'' version of the theorem. The paper consists of four sections: 1. The scalar case and the formulation of the main problem, 2. Preliminaries for the matrix case, 3. The one-step extension theorem for block Toeplitz matrices, and 4. The proof of Krein's theorem for orthogonal matrix polynomials. In Section 1 the authors study the Szegő orthogonal polynomials. The details about these polynomials and the proofs of Theorems 1.1 and 1.2, together with some references to related papers, can be found in the authors' recently published book ``Orthogonal systems and convolution operators'', Birkhäuser (2003; Zbl 1031.42021).
reviewed by: George Csordas
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47A20
zbMATH DE Number: 2021091
zbMATH Keywords: orthogonal matrix polynomials
zbMATH Keywords: zeros of matrix polynomials
zbMATH Keywords: block Toeplitz matrices
MaRDI profile type: Publication
full work available at URL: s00020-002-1153-4
OpenAlex ID: W1968582087
DOI: 10.1007/S00020-002-1153-4
description: scientific article; zbMATH DE number 2021091