### Abstract

It is known that all continuous orbital measures, μ,on a compact, connected, classical simple Lie group G or its Lie algebra satisfy a dichotomy: either μ^{k} εL^{2} or μ^{k} is purely singular to Haar measure. In this note we prove that the same dichotomy holds for the dual situation, continuous orbital measures on the complex group G ^{C}. We also determine the sharp exponent k such that any k-fold convolution product of continuous G-bi-invariant measures on G^{C} is absolute continuous with respect to Haar measure.

Original language | English |
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Pages (from-to) | 409-419 |

Number of pages | 11 |

Journal | Bolletino dell Unione Matematica Italiana |

Volume | 3 |

Issue number | 3 |

Publication status | Published - 2010 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Gupta, S. K., & Hare, K. E. (2010). L2- Singular dichotomy for orbital measures on complex groups.

*Bolletino dell Unione Matematica Italiana*,*3*(3), 409-419.