Elementary proof of a theorem of Helson
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- by Raouf Doss PDF
- Proc. Amer. Math. Soc. 27 (1971), 418-420 Request permission
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
- N. Bourbaki, Eléments de mathématique. XXI. Première partie: Les structures fondamentales de l’analyse. Livre VI: Intégration. Chapitre V: Intégration des mesures, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1244, Hermann & Cie, Paris, 1956 (French). MR 0084560
- Henry Helson, Fourier transforms on perfect sets, Studia Math. 14 (1954), 209–213 (1955). MR 68031, DOI 10.4064/sm-14-2-209-213
- 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
Additional Information
- © Copyright 1971 American Mathematical Society
- 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