Continuous singular measures with absolutely continuous convolution squares

Anthony H. Dooley; Sanjiv Kumar Gupta

doi:10.1090/s0002-9939-96-03391-6

Continuous singular measures with absolutely continuous convolution squares

Anthony H. Dooley, Sanjiv Kumar Gupta

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	3115-3122
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	124
Issue number	10
DOIs	https://doi.org/10.1090/s0002-9939-96-03391-6
Publication status	Published - 1996
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0002-9939-96-03391-6

Cite this

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title = "Continuous singular measures with absolutely continuous convolution squares",

abstract = "We prove for every non-abelian compact connected group G there is a continuous, singular, central measure μ with μ * μ in Lp for all p, 1 ≤ p ≤ ∞. 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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AU - Dooley, Anthony H.

AU - Gupta, Sanjiv Kumar

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AB - We prove for every non-abelian compact connected group G there is a continuous, singular, central measure μ with μ * μ in Lp for all p, 1 ≤ p ≤ ∞. 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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DO - 10.1090/s0002-9939-96-03391-6

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JO - Proceedings of the American Mathematical Society

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Continuous singular measures with absolutely continuous convolution squares

Abstract

ASJC Scopus subject areas

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