Central Fourier-Stieltjes transforms with an isolated value

Armstrong, Alan

doi:10.1090/S0002-9947-1980-0567088-0

Central Fourier-Stieltjes transforms with an isolated value
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Trans. Amer. Math. Soc. 259 (1980), 423-437 Request permission

Abstract:

Let $\mu$ be a central Borel measure on a compact, connected group G. If 0 is isolated in the range of ${\hat \mu }$, then there exists a closed, normal subgroup H of G such that ${\pi _H}\mu$, the restriction of $\mu$ to the cosets of H, is the convolution of an invertible measure with a nonzero idempotent measure. This result extends I. Glicksberg’s result for LCA groups. An example is given which shows that this result is false in general for disconnected groups.

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