An algorithm for the Hausdorff moment problem

1982 ◽  
Vol 39 (2) ◽  
pp. 231-238 ◽  
Author(s):  
G. Greaves
Keyword(s):  
Moment Problem ◽  
Hausdorff Moment Problem

scholarly journals The truncated matrix Hausdorff moment problem

2012 ◽  
Vol 19 (1) ◽  
pp. 21-42
Author(s):  
Sergey M. Zagorodnyuk
Keyword(s):  
Moment Problem ◽  
Hausdorff Moment Problem

4. The Hausdorff moment problem: regularization and error estimates

2002 ◽  
pp. 83-97
Author(s):  
Dang Dinh Ang ◽  
Rudolf Gorenflo ◽  
Vy Khoi Le ◽  
Dang Duc Trong
Keyword(s):  
Error Estimates ◽  
Moment Problem ◽  
Hausdorff Moment Problem

On the Hausdorff and Trigonometric Moment Problems

1961 ◽  
Vol 13 ◽  
pp. 454-461
Author(s):  
P. G. Rooney
Keyword(s):  
Moment Problem ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Functions Of Bounded Variation ◽  
Moment Problems ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Hausdorff Moment Problem

Let K be a subset of BV(0, 1)—the space of functions of bounded variation on the closed interval [0, 1]. By the Hausdorff moment problem for K we shall mean the determination of necessary and sufficient conditions that corresponding to a given sequence μ = {μn|n = 0, 1, 2, …} there should be a function α ∈ K so that(1)For various collections K this problem has been solved—see (3, Chapter III)By the trigonometric moment problem for K we shall mean the determination of necessary and sufficient conditions that corresponding to a sequence c = {cn|n = 0, ± 1, ± 2, …} there should be a function α ∈ K so that(2)For various collections K this problem has also been solved—see, for example (4, Chapter IV, § 4). It is noteworthy that these two problems have been solved for essentially the same collections K.

The Hausdorff Moment Problem with Complex Exponents and a Müntz-Szasz Theorem for Distributions

1997 ◽  
Vol 187 (1) ◽  
pp. 79-99
Author(s):  
Antonio J. Duran
Keyword(s):  
Moment Problem ◽  
Hausdorff Moment Problem

On Polynomial Maximum Entropy Method for Classical Moment Problem

2015 ◽  
Vol 8 (1) ◽  
pp. 117-127
Author(s):  
Jiu Ding ◽  
Noah H. Rhee ◽  
Chenhua Zhang
Keyword(s):  
Maximum Entropy ◽  
Moment Problem ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Moment Problems ◽  
Monomial Basis ◽  
Ill Conditioning ◽  
Legendre Moment ◽  
Hausdorff Moment Problem ◽  
Classical Moment Problem

AbstractThe maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis {1,x,x2,...,xn}. The maximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in. In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in and present the maximum entropy method for the Legendre moment problem. We also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments, respectively, and utilizing the corresponding maximum entropy method.

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