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On a general Tauberian theorem


Author: T. T. Moh
Journal: Proc. Amer. Math. Soc. 36 (1972), 167-172
MSC: Primary 40E05
DOI: https://doi.org/10.1090/S0002-9939-1972-0316935-7
MathSciNet review: 0316935
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Abstract: In this article the celebrated Tauberian theorem by Norbert Wiener ([1], [2]) is considerably extended by the introduction of a wider class of translation kernels. A number of applications are given to show the fruitfulness of this new generalization.


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  • [1] A. Beurling, Un théorème sur les fonctions bornées et uniformément continues sur l'axe réel, Acta Math. 77 (1945), 127-136. MR 7, 61. MR 0012701 (7:61f)
  • [2] N. Wiener, Tauberian theorem, Ann. of Math. 33 (1932), 1-100. MR 1503035
  • [3] W. B. Jurkat, Ein funktionentheoretischer Beweis für 0-Taubersätze bei den Verfahren non Borel und Euler-Knopp, Arch. Math. 7 (1956), 278-283. MR 18, 479. MR 0081987 (18:479c)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0316935-7
Keywords: Translation kernel, spectrum of $ \psi $
Article copyright: © Copyright 1972 American Mathematical Society

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