### Abstract

We show that the minimal k such that μ^{k} ∈ L^{1} (SU(n)) for all central, continuous measures μ on SU(n) is k = n. We do this by exhibiting an element g ∈ SU(n) for which the (n - 1)-fold product of its conjugacy class has zero Haar measure. This ensures that if μ_{g} is the corresponding orbital measure supported on the conjugacy class, then μ_{g}
^{n-1} is singular to L^{1}.

Original language | English |
---|---|

Pages (from-to) | 93-107 |

Number of pages | 15 |

Journal | Israel Journal of Mathematics |

Volume | 130 |

Publication status | Published - 2002 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Israel Journal of Mathematics*,

*130*, 93-107.

**Singularity of orbital measures in SU(n).** / Gupta, Sanjiv Kumar; Hare, Kathryn E.

Research output: Contribution to journal › Article

*Israel Journal of Mathematics*, vol. 130, pp. 93-107.

}

TY - JOUR

T1 - Singularity of orbital measures in SU(n)

AU - Gupta, Sanjiv Kumar

AU - Hare, Kathryn E.

PY - 2002

Y1 - 2002

N2 - We show that the minimal k such that μk ∈ L1 (SU(n)) for all central, continuous measures μ on SU(n) is k = n. We do this by exhibiting an element g ∈ SU(n) for which the (n - 1)-fold product of its conjugacy class has zero Haar measure. This ensures that if μg is the corresponding orbital measure supported on the conjugacy class, then μg n-1 is singular to L1.

AB - We show that the minimal k such that μk ∈ L1 (SU(n)) for all central, continuous measures μ on SU(n) is k = n. We do this by exhibiting an element g ∈ SU(n) for which the (n - 1)-fold product of its conjugacy class has zero Haar measure. This ensures that if μg is the corresponding orbital measure supported on the conjugacy class, then μg n-1 is singular to L1.

UR - http://www.scopus.com/inward/record.url?scp=0036350282&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036350282&partnerID=8YFLogxK

M3 - Article

VL - 130

SP - 93

EP - 107

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

ER -