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Restrictions of Fourier transforms of continuous measures


Author: Benjamin B. Wells
Journal: Proc. Amer. Math. Soc. 38 (1973), 92-94
MSC: Primary 43A46; Secondary 43A25
DOI: https://doi.org/10.1090/S0002-9939-1973-0315364-0
MathSciNet review: 0315364
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Abstract: Let $ G$ denote a compact abelian group and $ \Gamma $ its discrete dual. It is proved that $ E \subset \Gamma $ is Sidon if and only if the restriction to $ E$ of the algebra of Fourier transforms of continuous measures on $ G$ is all of $ {l_\infty }(E)$.


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

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  • [2] W. F. Eberlein, The point spectrum of weakly almost periodic functions, Michigan Math. J. 3 (1955–56), 137–139. MR 0082627
  • [3] I. Glicksberg and I. Wik, The range of Fourier-Stieltjes transforms of parts of measures, Conference on Harmonic Analysis (Univ. Maryland, College Park, Md., 1971), Springer, Berlin, 1972, pp. 73–77. Lecture Notes in Math., Vol. 266. MR 0433145
  • [4] 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/S0002-9939-1973-0315364-0
Keywords: Fourier transform, Sidon set
Article copyright: © Copyright 1973 American Mathematical Society