Work

A functional approach to lower bounds for numerical series

Year: 2025

Type: article

Abstract: In this work, we investigate lower bounds for real-valued series of the form ∑ n ≥ 0 a n , with particular emphasis on the case where the associated linear functional, defined through the sequence of moments ( a n ) n ≥ 0 , is positive. We examine how this positivity condition impacts the derivation of lower bounds for the series, utilizing techniques from functional analysis. By considering both general lower bounds and those dependent on specific properties of the sequence, we provide a comprehensive framework for understanding the convergence and asymptotic behavior of such numerical series. Special attention is given to the role of moment sequences, Hankel determinants, and their connections to the underlying functional structure. The results offer novel insights into the convergence criteria and the possible acceleration of series summation.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2025.130199

Authors: Youssef Esstafa, Ridha Sfaxi

Institutions: Le Mans Université, Laboratoire Manceau de Mathématiques, University of Gabès

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Conseil Régional des Pays de la Loire