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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.
The Journal of Analysis – Springer Journals
Published: Jun 1, 2023
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
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