Remarks on converse Carleman and Krein criteria for the classical moment problem
type: Item
instance of: scholarly article
title: Remarks on converse Carleman and Krein criteria for the classical moment problem
zbMATH Open document ID: 0992.44003
DOI: 10.1017/S1446788700002731
author: Anthony G. Pakes
published in: Journal of the Australian Mathematical Society
publication date: 2002-09-11T00:00:00Z
Mathematics Subject Classification ID: 44A20
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 1659328
zbMATH Keywords: Carleman and Krein conditions
zbMATH Keywords: Hamburger and Stieltjes moment problems
MaRDI profile type: Publication
cites work: On the moment problems
cites work: Length biasing and laws equivalent to the log-normal
cites work: Q3141900
cites work: SOME REMARKS ON THE MOMENT PROBLEM (I)
cites work: Q3922907
cites work: A maximum entropy approach to the classical moment problem
cites work: Indeterminate moment problems and the theory of entire functions
cites work: Krein condition in probabilistic moment problems
cites work: The moment problem for polynomial forms in normal random variables
cites work: A note on the Carleman condition for determinacy of moment problems
cites work: Q4301585
cites work: On Krein's theorem for indeterminacy of the classical moment problem
cites work: Criteria for the Unique Determination of Probability Distributions by Moments
cites work: Characterization by invariance under length-biasing and random scaling
review text: The paper deals with the Carleman and Krein conditions for the Hamburger and Stieltjes moment problems. The author reviews and discusses these conditions and the connection to some results of \textit{P. Koosis} [The logarithmic integral. Vol. I., Cambridge University Press, Cambridge (1988; Zbl 0665.30038)] and \textit{G. D. Lin} [Stat. Probab. Lett. 35, No. 1, 85-90 (1997; Zbl 0904.62021)]. The principle aim of the paper is to provide an unified account of the Koosis and Lin results and to generalize them. The author also simplifies and streamlines some existing proofs.
reviewed by: Khristo N. Boyadzhiev
description: scientific article; zbMATH DE number 1659328