On the Moment Problem and Related Problems

Octav Olteanu
Additional contact information
Octav Olteanu: Department Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, Romania

Mathematics, 2021, vol. 9, issue 18, 1-26

Abstract: 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 ( y j ) j ? ? n of real numbers and a closed subset F ? ? n , n ? { 1 , 2 , … } , find a positive regular Borel measure ? on F such that ? F t j d ? = y j , j ? ? n . This is the full moment problem. The existence, uniqueness, and construction of the unknown solution ? are the focus of attention. The numbers y j , j ? ? n are called the moments of the measure ? . 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 y j 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.

Keywords: full moment problem; polynomial approximation; unbounded subsets; moment-determinate measure; Markov moment problem; quadratic forms; self-adjoint operator; truncated moment problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/18/2289/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/18/2289/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:18:p:2289-:d:637373

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().