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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
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.

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Keywords: Invertible measure, locally compact Abelian group, Fourier transform
Article copyright: © Copyright 1974 American Mathematical Society

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