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Transactions of the American Mathematical Society

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Unitary measures on LCA groups


Author: Lawrence Corwin
Journal: Trans. Amer. Math. Soc. 196 (1974), 425-430
MSC: Primary 43A10
DOI: https://doi.org/10.1090/S0002-9947-1974-0358219-3
MathSciNet review: 0358219
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Abstract: A unitary measure on a locally compact Abelian (LCA) group G is a complex measure whose Fourier transform is of absolute value 1 everywhere. The problem of finding all such measures is known to be closely related to that of finding all invertible measures on G. In this paper, we find all unitary measures when G is the circle or a discrete group. If G is a torsion-free discrete group, the characterization generalizes a theorem of Bohr.


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

  • [1] H. Bohr, Über fastperodische ebene Bewegungen, Comment. Math. Helv. 4 (1934), 51-64. MR 1509444
  • [2] I. Glicksberg, A remark on a theorem of Beurling and Helson, Proc. Amer. Math. Soc. 10 (1959), 587. MR 22 #12347. MR 0121612 (22:12347)
  • [3] S. T. Hu, Homotopy theory, Pure and Appl. Math., vol. 8, Academic Press, New York, 1959. MR 21 #5186. MR 0106454 (21:5186)
  • [4] P. Huber, Homotopical cohomology and Čech cohomology, Math. Ann. 144 (1961), 73-76. MR 24 #A3646. MR 0133821 (24:A3646)
  • [5] W. Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Appl. Math., no. 12, Interscience, New York, 1962. MR 27 #2808. MR 0152834 (27:2808)
  • [6] N. Steenrod, Universal homology groups, Amer. J. Math. 58 (1936), 661-701. MR 1507191
  • [7] J. Taylor, Inverses, logarithms, and idempotents in $ M(G)$, Rocky Mountain J. Math. 2 (1972), no. 2, 183-206. MR 45 #5669. MR 0296610 (45:5669)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0358219-3
Keywords: Invertible measure, locally compact Abelian group, Fourier transform
Article copyright: © Copyright 1974 American Mathematical Society

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