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Selected Topics in Approximation and Computation$
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Marek A. Kowalski, Krzystof A. Sikorski, and Frank Stenger

Print publication date: 1995

Print ISBN-13: 9780195080599

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195080599.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 27 September 2021

Moment Problems

Moment Problems

Chapter:
(p.169) Chapter 5 Moment Problems
Source:
Selected Topics in Approximation and Computation
Author(s):

Marek A. Kowalski

Krzysztof A. Sikorski

Frank Stenger

Publisher:
Oxford University Press
DOI:10.1093/9780195080599.003.0008

In this chapter we present the classical moment problems as they have been mathematically defined. Moment problems are the simplest way to describe inverse problems mathematically. These problems were originally posed with moments being integrals of monomials. Such moment problems are ill-posed, and present considerable computational difficulty. On the other hand, moment problems whose moments are integrals of orthogonal bases can computationally be dealt with much more easily.

Keywords:   Banach, Chakalov, Darboux, Favard, Gauss, Helly theorems, Mazur-Orlicz theorem, Riesz-Steinhauss theorem, Stieltjes inversion formula

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