M. G. Krein's ideas in the theory of orthogonal polynomials
type: Item
instance of: scholarly article
title: M. G. Krein's ideas in the theory of orthogonal polynomials
zbMATH Open document ID: 0852.42008
DOI: 10.1007/BF01057002
published in: Ukrainian Mathematical Journal
publication date: 1995-11-02T00:00:00Z
review text: Mark Grigorievich Krein surely made various relevant contributions to the theory of orthogonal polynomials, starting with his investigations of the spectra of Jacobi matrices in the problem of harmonic oscillations of certain mechanical systems. Some of Krein's contributions are sketched in this paper. Among them are Krein's theorem which characterizes orthogonal polynomials on the real line with a measure supported on a set with a finite number of accumulation points, Krein's initiation of matrix and operator moment problems, Krein's contribution to the extension of Szegö's theorem for orthogonal polynomials on the unit circle, and finally Krein's complete description of the zeros of orthogonal polynomials on the unit circle with an indefinite weight.
reviewed by: Walter Van Assche
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 42-03
Mathematics Subject Classification ID: 01A60
zbMATH DE Number: 803819
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Jacobi matrices
zbMATH Keywords: operator moment problems
zbMATH Keywords: Szegö's theorem
zbMATH Keywords: zeros
author: B. P. Osilenker
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 803819