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Elementary proof of a theorem of Helson


Author: Raouf Doss
Journal: Proc. Amer. Math. Soc. 27 (1971), 418-420
MSC: Primary 42.58
DOI: https://doi.org/10.1090/S0002-9939-1971-0271644-7
MathSciNet review: 0271644
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Abstract: An elementary proof is given of a theorem of Helson, to the effect that in a locally compact abelian group, the transform of a measure concentrated on a Helson set does not vanish at infinity.


References [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Livre VI: Intégration, Chapitre 5, Actualités Sci. Indust., no. 1244, Hermann, Paris, 1956. MR 18, 881. MR 0084560 (18:881c)
  • [2] H. Helson, Fourier transforms on perfect sets, Studia Math. 14 (1954), 209-213. MR 16, 817. MR 0068031 (16:817c)
  • [3] W. Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Appl. Math., no. 12, Interscience, New York, 1962. MR 27 #2808. MR 0152834 (27:2808)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0271644-7
Keywords: Locally compact abelian group, Helson set, Fourier-Steiltjes transform of a measure
Article copyright: © Copyright 1971 American Mathematical Society

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