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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Bohr compactification and continuous measures


Author: Sadahiro Saeki
Journal: Proc. Amer. Math. Soc. 80 (1980), 244-246
MSC: Primary 43A25; Secondary 43A46
MathSciNet review: 577752
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Abstract: Let G be an LCA group with dual $ \Gamma $. As a consequence of our main result, it is shown that every continuous regular measure $ \mu $ concentrated on a Kronecker set and with $ {\text{norm}} > 1$ has the property that $ \{ \vert\hat \mu \vert > 1\} $ is dense in the Bohr compactification of $ \Gamma $.


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

  • [1] Edwin Hewitt and Shizuo Kakutani, A class of multiplicative linear functionals on the measure algebra of a locally compact Abelian group, Illinois J. Math. 4 (1960), 553–574. MR 0123198
  • [2] 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
  • [3] Y. Katznelson, Sequences of integers dense in the Bohr group, Proc. Roy. Inst. Tech. (Stockholm) (1973), 79-86.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0577752-0
Keywords: Bohr compactification, continuous measure, Kronecker set, $ {K_p}$-set
Article copyright: © Copyright 1980 American Mathematical Society