Unique solvability of an extended Hamburger moment problem
type: Item
instance of: scholarly article
title: Unique solvability of an extended Hamburger moment problem
zbMATH Open document ID: 0654.42024
DOI: 10.1016/0022-247X(87)90011-4
author: Olav Njåstad
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: R-functions are rational functions with no poles in the extended complex plane outside a given set \(\{a_ 1,...,a_ p\}\) of points on the real axis. Methods from the theory of orthogonal polynomials can be extended to R-functions. By this means the author solved an extended Hamburger moment problem: Given sequences of real numbers \(\{c_ n^{(i)}:n=1,2,...\}\), \(i=1,...,p\), find conditions for a distribution function \(\psi\) to exist such that \(\int^{\infty}_{-\infty}d\psi (t)=1,\quad \int^{\infty}_{-\infty}d\psi (t)/(t-a_ i)^ m=c_ m^{(i)},\) \(m=1,2,...,i=1,...,p\). In this paper these methods are extended to treat conditions for the moment problem to have a unique solution. The results are related to the classical limit point-limit circle situation.
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 4067558
zbMATH Keywords: unique solvability
zbMATH Keywords: R-functions
zbMATH Keywords: extended Hamburger moment problem
zbMATH Keywords: point-limit circle
MaRDI profile type: Publication
cites work: Q5859156
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full work available at URL: 0022-247x(87)90011-4
OpenAlex ID: W2080899430
description: scientific article; zbMATH DE number 4067558