Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 66, Number 1 (2014), 317-348.
Riesz measures and Wishart laws associated to quadratic maps
We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset$ R$^n$ is a regular open convex cone. In this context we prove new general formulas for moments of the Wishart laws on non-symmetric cones. For homogeneous cases, all the quadratic maps are characterized and the associated Riesz measure and Wishart law with its moments are described explicitly. We apply the theory of relatively invariant distributions and a matrix realization of homogeneous cones obtained recently by the second author.
J. Math. Soc. Japan, Volume 66, Number 1 (2014), 317-348.
First available in Project Euclid: 24 January 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H05: Characterization and structure theory
Secondary: 15B48: Positive matrices and their generalizations; cones of matrices 43A35: Positive definite functions on groups, semigroups, etc.
GRACZYK, Piotr; ISHI, Hideyuki. Riesz measures and Wishart laws associated to quadratic maps. J. Math. Soc. Japan 66 (2014), no. 1, 317--348. doi:10.2969/jmsj/06610317. https://projecteuclid.org/euclid.jmsj/1390600847