The Dichotomy Problem for Orbital Measures of SU(n) |
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| Authors: | Sanjiv Gupta and Kathryn E. Hare |
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| Affiliation: | (1) University of Wisconsin, Madison, Madison, WI, U.S.A.;(2) Princeton University, Princeton, NJ, U.S.A.;(3) University of Georgia, Athens, Athens, GA, U.S.A. |
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| 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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