标题： 里斯测度和与二次映射相关的维希特定律 显示英文标题

标题： Riesz measures and Wishart laws associated to quadratic maps

摘要： 我们引入了与一个$\Omega$-正（虚拟）二次映射相关的Riesz测度和Wishart律的一个自然定义，其中$\Omega \subset \real^n$是一个正则开凸锥。 我们给出了Wishart律矩的一般公式。 此外，如果二次映射在作用于锥$\Omega$的线性群的作用下具有等变性质，则通过利用齐次锥上相对不变分布的理论，可以显式地描述相应的Riesz测度和Wishart律。 显示英文摘要

摘要： We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset \real^n$ is a regular open convex cone. We give a general formula for moments of the Wishart laws. Moreover, if the quadratic map has an equivariance property under the action of a linear group acting on the cone $\Omega$ transitively, then the associated Riesz measure and Wishart law are described explicitly by making use of theory of relatively invariant distributions on homogeneous cones.