B P International

A Recent and Modern Approach to The Moment Problem on R

Moussoda Toure1, Gane Samb Lo1,2,3∗ and Aladji Babacar Niang1

1LERSTAD, Gaston Berger University, Saint-Louis, Senegal.
2LSTA, Pierre and Marie Curie University, Paris VI, France.
3AUST – African University of Science and Technology, Abuja, Nigeria.

Abstract

The moment problem is an important problem in Functional Analysis and in Probability measure. It goes back to Stieltjes, around 1890. There is still an important ongoing interest in the recent literature. But, up today, the main theoretical resource (Shohat and Tamarkin, 1934) does not have the modern exposure it deserves, especially in the current development of measure theory of integration. Besides, the multivariate version is far less exploited. In this paper, a full exposure of such a theory is presented, using the latest knowledge of measure theory and functional analysis. As a result, the basis of future development is layed out and the accessibility of the theory by modern graduate students and researchers is guaranteed.

Keywords: Moment problems; ordered Hahn-Banach theorem version; probability measures characterizations by moments; weak convergence using moments.

ISBN: 978-93-90149-72-8 (Print) | 978-93-90149-22-3 (eBook)

Chapter DOI: https://doi.org/10.9734/bpi/tpmcs/v1/5054D

Volume DOI: https://doi.org/10.9734/bpi/tpmcs/v1

Published: August 17, 2020

Complete book available here: http://bp.bookpi.org/index.php/bpi/catalog/book/237