Bohr compactification and continuous measures
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- by Sadahiro Saeki PDF
- Proc. Amer. Math. Soc. 80 (1980), 244-246 Request permission
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 $\{ |\hat \mu | > 1\}$ is dense in the Bohr compactification of $\Gamma$.References
- 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 123198
- 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 Y. Katznelson, Sequences of integers dense in the Bohr group, Proc. Roy. Inst. Tech. (Stockholm) (1973), 79-86.
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 244-246
- MSC: Primary 43A25; Secondary 43A46
- DOI: https://doi.org/10.1090/S0002-9939-1980-0577752-0
- MathSciNet review: 577752