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arXiv · 1206.6091

The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem

Bartosz Kołodziejek
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Abstract

We prove the Lukacs characterization of the Wishart distribution on non-octonion symmetric cones of rank greater than 2. We weaken the smoothness assumptions in the version of the Lukacs theorem of [Bobecka-Weso{\l}owski, Studia Math. 152 (2002), 147-160]. The main tool is a new solution of the Olkin-Baker functional equation on symmetric cones, under the assumption of continuity of respective functions. It was possible thanks to the use of Gleason's theorem.

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Bartosz Kołodziejek. 2012-06-26. The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem. https://doi.org/10.4064/sm217-1-1

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