Operator-Stable Laws: Multiple Exponents and Elliptical Symmetry

Abstract

We characterize the class of linear operators on a finite dimensional inner product space which are the exponents of a full operator-stable law. This answers a question of Paulauskas [6] concerning those operator-stable laws whose characteristic functions are the exponential of quadratic forms. The symmetry group of such laws must be conjugate to the group of all orthogonal transformations on the space.