Continuous singular measures with absolutely continuous convolution squares

Dooley, Anthony; Gupta, Sanjiv

doi:10.1090/S0002-9939-96-03391-6

Continuous singular measures with absolutely continuous convolution squares
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by Anthony H. Dooley and Sanjiv Kumar Gupta PDF

Proc. Amer. Math. Soc. 124 (1996), 3115-3122 Request permission

Abstract:

We prove for every non-abelian compact connected group $G$ there is a continuous, singular, central measure $\mu$ with $\mu *\mu$ in $L^{p}$ for all $p, 1 \leq p < \infty$. We also construct such measures on some families of non-abelian compact totally disconnected groups. These results settle an open question of Ragozin.

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