对称锥上的Lukacs-Olkin-Rubin定理
The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem
摘要：
证明了秩大于2的非八元数对称锥上Wishart分布的Lukacs特征。我们削弱了[Bobecka-Wesoenchowski，Studia Math.152（2002），147-160]中卢卡奇定理的光滑性假设。主要工具是对称锥上的Olkin-Baker函数方程的一个新的解决方案，假设各自的功能连续。这要归功于格里森定理的运用。
英文摘要：
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-Wesołowski, 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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