On M. G. Krein's contribution to the moment problem
type: Item
instance of: scholarly article
title: On M. G. Krein's contribution to the moment problem
zbMATH Open document ID: 0859.44005
DOI: 10.1007/BF01057001
author: A. A. Nudel'man
published in: Ukrainian Mathematical Journal
publication date: 1995-11-02T00:00:00Z
review text: The author gives a survey of scientific results of the famous mathematician M. G. Krein connected with his contribution to the moment problem. The paper contains 6 sections and detailed references of his works and related topics. The author discusses Krein's results starting from his first works with N. Akhiezer in 1934-1938 that were devoted to the problems connected with Fourier coefficients of bounded real functions. Further, Krein's results in the framework of another approach, the theory of canonical solutions and ``limiting values'' of integrals are given, the generalization of the results of the St. Petersburg School is presented. The author discusses in detail other of their joint results in the theory of ``limiting integrals'' and surveys Krein's results in the \(L\)-problem in abstract linear normed spaces, in continuative analog of the trigonometric and power moment problems and also announces some applications to his mechanical interpretation of Stieltjes' investigation of the moment problem and continued fractions.
Mathematics Subject Classification ID: 44A60
Mathematics Subject Classification ID: 42A70
Mathematics Subject Classification ID: 44-03
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 42A16
Mathematics Subject Classification ID: 01A70
zbMATH DE Number: 803818
zbMATH Keywords: M. G. Krein
zbMATH Keywords: limiting values of integrals
zbMATH Keywords: \(L\)-problem
zbMATH Keywords: trigonometric moment problem
zbMATH Keywords: Leningrad school
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: St. Petersburg School
zbMATH Keywords: power moment problems
zbMATH Keywords: continued fractions
reviewed by: S. Yakubovich
MaRDI profile type: Publication
cites work: Q5802676
cites work: Q5534404
cites work: Q4163734
cites work: Q4103986
cites work: Q4744838
cites work: Q3980303
full work available at URL: https://doi.org/10.1007/bf01057001
OpenAlex ID: W4246957170
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description: scientific article; zbMATH DE number 803818