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On a theorem of E. Lukacs

Author: Paul Embrechts
Journal: Proc. Amer. Math. Soc. 68 (1978), 292-294
MSC: Primary 43A25; Secondary 44A35, 60B15
Erratum: Proc. Amer. Math. Soc. 75 (1979), 375.
MathSciNet review: 0470617
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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 [Enhancements On Off] (What's this?)

  • [1] E. Lukacs, An essential property of the Fourier transforms of distribution functions, Proc. Amer. Math. Soc. 3 (1952), 508-510. MR 13, 937. MR 0047817 (13:937b)
  • [2] -, 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. MR 29 #4082. MR 0166809 (29:4082)
  • [3] -, Characteristic functions, 2nd ed., Griffin, London, 1970.
  • [4] W. Rudin, Fourier analysis on groups, Interscience, New York, 1970. MR 0152834 (27:2808)

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Keywords: L.C.A. group, integral transform, convolution and uniqueness property
Article copyright: © Copyright 1978 American Mathematical Society

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