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Proceedings of the American Mathematical Society

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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, Eléments de mathématique. XXI. Première partie: Les structures fondamentales de l’analyse. Livre VI: Intégration. Chapitre V: Intégration des mesures, Actualités Sci. Ind., no. 1244, Hermann & Cie, Paris, 1956 (French). MR 0084560
  • [2] Henry Helson, Fourier transforms on perfect sets, Studia Math. 14 (1954), 209–213 (1955). MR 0068031
  • [3] Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962. MR 0152834

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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