On a theorem of E. Lukacs
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- by Paul Embrechts
- Proc. Amer. Math. Soc. 68 (1978), 292-294
- DOI: https://doi.org/10.1090/S0002-9939-1978-0470617-5
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Erratum: Proc. Amer. Math. Soc. 75 (1979), 375.
Abstract:
We prove that an integral transform of measures on a locally compact abelian group, which satisfies both the uniqueness and the convolution property, is closely related to the Fourier-Stieltjes transform. This extends a result obtained by Lukacs for the real line.References
- Eugene Lukacs, An essential property of the Fourier transforms of distribution functions, Proc. Amer. Math. Soc. 3 (1952), 508–510. MR 47817, DOI 10.1090/S0002-9939-1952-0047817-3
- Eugene Lukacs, A linear mapping of the space of distribution functions onto a set of bounded continuous functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 1–6 (1964). MR 166809, DOI 10.1007/BF00531679 —, Characteristic functions, 2nd ed., Griffin, London, 1970.
- Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 292-294
- MSC: Primary 43A25; Secondary 44A35, 60B15
- DOI: https://doi.org/10.1090/S0002-9939-1978-0470617-5
- MathSciNet review: 0470617