Geodesic
The Lukacs–Olkin–Rubin theorem on symmetric cones through Gleason's theorem
Bartosz Kołodziejek1
1 Faculty of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa, Poland
Studia Mathematica, Tome 217 (2013) no. 1, pp. 1-17 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm217-1-1
Keywords: prove lukacs characterization wishart distribution non octonion symmetric cones rank greater weaken smoothness assumptions version lukacs theorem bobecka weso owski studia math main tool solution olkin baker functional equation symmetric cones under assumption continuity respective functions possible thanks gleasons theorem

Bartosz Kołodziejek 1

1 Faculty of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa, Poland 
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 through {Gleason's} theorem},
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 through Gleason's theorem
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 through Gleason's theorem
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Bartosz Kołodziejek. The Lukacs–Olkin–Rubin theorem on symmetric cones
 through Gleason's theorem. Studia Mathematica, Tome 217 (2013) no. 1, pp. 1-17. doi: 10.4064/sm217-1-1

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