### 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 |

Publication status | Published - 1996 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*124*(10), 3115-3122.

**Continuous singular measures with absolutely continuous convolution squares.** / Dooley, Anthony H.; Gupta, Sanjiv Kumar.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 124, no. 10, pp. 3115-3122.

}

TY - JOUR

T1 - Continuous singular measures with absolutely continuous convolution squares

AU - Dooley, Anthony H.

AU - Gupta, Sanjiv Kumar

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21444455605&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21444455605&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21444455605

VL - 124

SP - 3115

EP - 3122

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 10

ER -