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

• Autorzy: Bartosz Kołodziejek
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 62H05: Characterization and structure theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 217
• Numer: 1
• Strony: 1-17

Daty

wydano

2013

Twórcy

autor

Bartosz Kołodziejek

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/sm217-1-1