New uniqueness conditions for the classical moment problem
type: Item
instance of: scholarly article
title: New uniqueness conditions for the classical moment problem
zbMATH Open document ID: 1349.44004
DOI: 10.1134/S0001434612110259
published in: Mathematical Notes
publication date: 2013-04-15T00:00:00Z
review text: According to the author, in a symmetric space \(E\) on (0,1] (Marcinkiewicz and Orlicz spaces are symmetric) there is \textit{uniqueness in the Hamburger moment problem} if the conditions \(x\in E\) and \(\int_0^1x(t)^ndt=\int_0^1y(t)^ndt\) for all integers \(n\geq1\) imply \(\mu\{t:x(t)>\tau\}=\mu\{t:y(t)>\tau\}\) for all real numbers \(\tau\), where \(\mu\) is the Lebesgue measure. The author characterizes some Marcinkiewicz and Orlicz spaces having this property. Similar results are given, related to the \textit{uniqueness in the Stieltjes moment problem}. Some ideas from the theory of extrapolation, due to \textit{B. Jawerth} and \textit{M. Milman} [Mem. Am. Math. Soc. 440 (1991; Zbl 0733.46040)], are used.
reviewed by: Florian-Horia Vasilescu
Mathematics Subject Classification ID: 44A60
Mathematics Subject Classification ID: 47A57
zbMATH DE Number: 6153814
zbMATH Keywords: power moment problem
zbMATH Keywords: uniqueness conditions due to Carleman
zbMATH Keywords: conditions for the well-posedness due to Cramer and Krein
zbMATH Keywords: extrapolation of spaces and operators
zbMATH Keywords: symmetric space
zbMATH Keywords: Marcinkiewicz space
zbMATH Keywords: Orlicz space
author: K. V. Lykov
MaRDI profile type: Publication
cites work: Q3254471
cites work: Notes on Fourier analysis. XXIX. An extrapolation theorem
cites work: Extrapolation theory with applications
cites work: Q4891389
cites work: Q5401276
cites work: Some remarks on the moment problem and its relation to the theory of extrapolation of spaces
cites work: Q5437065
cites work: Determinate multidimensional measures, the extended Carleman theorem and quasi-analytic weights
description: scientific article; zbMATH DE number 6153814