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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On a tauberian theorem of Wiener and Pitt


Author: Harold G. Diamond
Journal: Proc. Amer. Math. Soc. 31 (1972), 152-158
MSC: Primary 40E05
MathSciNet review: 0294944
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Abstract: N. Wiener and H. R. Pitt established a tauberian theorem which is ``intermediate'' between that of Wiener and Ikehara on one hand and a theorem of Hardy and Littlewood on the other. A new proof of the Wiener-Pitt theorem is given, using a technique of Bochner.


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  • [1] V. G. Avakumović, Théorèmes relatifs aux intégrales de Laplace sur leur frontiêre de convergence, C. R. Acad. Sci. Paris 204 (1937), 224-226.
  • [2] P. Lévy, Sur une application de la dérivée d'ordre non entier au calcul des probabilités, C. R. Acad. Sci. Paris 176 (1923), 1118-1120.
  • [3] H. R. Pitt, Tauberian theorems, Tata Institute of Fundamental Research, Monographs on Mathematics and Physics, vol. 2, Oxford University Press, London, 1958. MR 0106376 (21 #5109)
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  • [6] N. Wiener and H. R. Pitt, A generalization of Ikehara's theorem, J. Math. Phys. 17 (1939), 247-258.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0294944-4
PII: S 0002-9939(1972)0294944-4
Keywords: Tauberian theorem, Laplace transform, Wiener-Ikehara theorem
Article copyright: © Copyright 1972 American Mathematical Society