classical moment problem
Recently Published Documents


TOTAL DOCUMENTS

28
(FIVE YEARS 2)

H-INDEX

10
(FIVE YEARS 0)

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2289
Author(s):  
Octav Olteanu

Firstly, we recall the classical moment problem and some basic results related to it. By its formulation, this is an inverse problem: being given a sequence (yj)j∈ℕn  of real numbers and a closed subset F⊆ℝn, n∈{1,2,…}, find a positive regular Borel measure μ on F such that ∫Ftjdμ=yj, j∈ℕn. This is the full moment problem. The existence, uniqueness, and construction of the unknown solution μ are the focus of attention. The numbers yj, j∈ℕn are called the moments of the measure μ. When a sandwich condition on the solution is required, we have a Markov moment problem. Secondly, we study the existence and uniqueness of the solutions to some full Markov moment problems. If the moments yj are self-adjoint operators, we have an operator-valued moment problem. Related results are the subject of attention. The truncated moment problem is also discussed, constituting the third aim of this work.



2020 ◽  
Vol 11 (1) ◽  
pp. 25-29
Author(s):  
A.S. Mikhaylov ◽  
V.S. Mikhaylov




Author(s):  
Jonathan Eckhardt ◽  
Aleksey Kostenko




2015 ◽  
Vol 8 (1) ◽  
pp. 117-127
Author(s):  
Jiu Ding ◽  
Noah H. Rhee ◽  
Chenhua Zhang

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.



2012 ◽  
Vol 92 (5-6) ◽  
pp. 797-806 ◽  
Author(s):  
K. V. Lykov


Sign in / Sign up

Export Citation Format

Share Document