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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.
- [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)
- [4]
G. Pólya, On the zeros of an integral function represented by Fourier's integral, Messenger Math. 52 (1923), 185-188.
- [5]
E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford Univ. Press, London, 1937.
- [6]
N. Wiener and H. R. Pitt, A generalization of Ikehara's theorem, J. Math. Phys. 17 (1939), 247-258.
- [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 Math. and Physics, no. 2, Oxford Univ. Press, London, 1958. MR 21 #5109. MR 0106376 (21:5109)
- [4]
- G. Pólya, On the zeros of an integral function represented by Fourier's integral, Messenger Math. 52 (1923), 185-188.
- [5]
- E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford Univ. Press, London, 1937.
- [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
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