Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications

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

Mathematics, 2020, vol. 8, issue 10, 1-12

Abstract: This paper starts by recalling the author’s results on polynomial approximation over a Cartesian product A of closed unbounded intervals and its applications to solving Markov moment problems. Under natural assumptions, the existence and uniqueness of the solution are deduced. The characterization of the existence of the solution is formulated by two inequalities, one of which involves only quadratic forms. This is the first aim of this work. Characterizing the positivity of a bounded linear operator only by means of quadratic forms is the second aim. From the latter point of view, one solves completely the difficulty arising from the fact that there exist nonnegative polynomials on ? n , n ≥ 2 , which are not sums of squares.

Keywords: polynomial approximation; Hahn–Banach theorem; Markov moment problem; determinacy; quadratic forms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/10/1654/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/10/1654/ (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:8:y:2020:i:10:p:1654-:d:419538

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 ().