Abstract.
For many orbital measures μ, on SU(n), we show that either μk ∈ L2 or μk is singular to L1. The least k for which μk ∈ L2 is determined and is shown to be the minimum k for which the k-fold product of the conjugacy class supporting the measure has positive measure. It would be interesting to know if all orbital measures satisfy this dichotomy.
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Gupta, S., Hare, K. The Dichotomy Problem for Orbital Measures of SU(n). Mh Math 146, 227–238 (2005). https://doi.org/10.1007/s00605-005-0321-4
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DOI: https://doi.org/10.1007/s00605-005-0321-4