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On the convergence of weighted mean summable improper integrals over R≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}_{\ge 0}$$\end{document}

On the convergence of weighted mean summable improper integrals over... Given a real-valued function a(x) which is locally integrable in the sense of Lebesgue over R≥0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb {R}}_{\ge 0}$$\end{document}, we obtain Tauberian conditions for the convergence of the integral ∫0∞a(t)dt\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\int _{0}^{\infty }a(t)\,dt$$\end{document} out of the weighted mean summability. Furthermore, we discuss summability of improper integrals via iterations of weighted means and provide corresponding Tauberian theorems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

On the convergence of weighted mean summable improper integrals over R≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}_{\ge 0}$$\end{document}

The Journal of Analysis , Volume OnlineFirst – Sep 21, 2022

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to The Forum D’Analystes 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-022-00501-2
Publisher site
See Article on Publisher Site

Abstract

Given a real-valued function a(x) which is locally integrable in the sense of Lebesgue over R≥0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb {R}}_{\ge 0}$$\end{document}, we obtain Tauberian conditions for the convergence of the integral ∫0∞a(t)dt\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\int _{0}^{\infty }a(t)\,dt$$\end{document} out of the weighted mean summability. Furthermore, we discuss summability of improper integrals via iterations of weighted means and provide corresponding Tauberian theorems.

Journal

The Journal of AnalysisSpringer Journals

Published: Sep 21, 2022

Keywords: Weighted mean summability of integrals; Lebesgue integral; Improper integrals over R≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}_{\ge 0}$$\end{document}; Tauberian conditions; Iterated weighted means; Forward and backward differences; 40A10; 40C10; 40E05; 26D15

References