On a tauberian theorem of Wiener and Pitt
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- by Harold G. Diamond PDF
- Proc. Amer. Math. Soc. 31 (1972), 152-158 Request permission
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.References
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V. G. Avakumović, Théorèmes relatifs aux intégrales de Laplace sur leur frontiêre de convergence, C. R. Acad. Sci. Paris 204 (1937), 224-226.
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.
- H. R. Pitt, Tauberian theorems, Tata Institute of Fundamental Research, Monographs on Mathematics and Physics, vol. 2, Oxford University Press, London, 1958. MR 0106376 G. Pólya, On the zeros of an integral function represented by Fourier’s integral, Messenger Math. 52 (1923), 185-188. E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford Univ. Press, London, 1937. N. Wiener and H. R. Pitt, A generalization of Ikehara’s theorem, J. Math. Phys. 17 (1939), 247-258.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 152-158
- MSC: Primary 40E05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294944-4
- MathSciNet review: 0294944