Abstract
In this paper, we give a simple alternative proof of a Tauberian theorem of Hardy and Littlewood (Theorem E stated below, [3]).
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References
Ananda-Rau K, On the converse of Abel’s theorem,J. London Math. Soc. 3 (1928) 200–205
Hardy G H,Divergent Series (Oxford) (1949)
Hardy G H and Littlewood J E, A further note on the converse of Abel’s theorem,Proc. London Math. Soc. 25(2) (1926) 219–236
Landau E, über die Konvergenz einiger Klassen von unendlichen Reihen am Rande des Konvergenzgebietes,Monatshefte für Math. und Phys. 18 (1907) 8–28
Littlewood J E, The converse of Abel’s theorem on power series,Proc. London Math. Soc. 9(2) (1910) 434–448
Pati T, Remarks on some Tauberian theorems of Littlewood, Hardy and Littlewood, Vijayaraghavan and Ananda-Rau (forthcoming inJ. Nat. Acad. Math., Gorakhpur)
Tauber A, Ein satz der Theorie der unendlichen Reihen,Monatshefte für Math. und Phys. 8 (1897) 273–277
Vijayaraghavan T, A Tauberian theorem,J. London Math. Soc. 2 (1926) 113–120
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Pati, T. On a tauberian theorem of Hardy and Littlewood. Proc. Indian Acad. Sci. (Math. Sci.) 111, 221–227 (2001). https://doi.org/10.1007/BF02829592
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DOI: https://doi.org/10.1007/BF02829592