The symmetry group and exponents of operator stable probability measures
Let \(\mu\) be an operator-stable probability measure on a finite- dimensional real vector space \({\mathcal V}\). The role of the index in the one-dimensional case is played by an invertible linear operator \({\mathcal B}\) on \({\mathcal V}\) called the exponent of \(\mu\). There exist exponents of \(\mu\) which commute with every operator in the measure's symmetry group. This result is used to find the representation of the Levy measure of \(\mu\) which does not depend on the choice of an exponent.
scientific article; zbMATH DE number 3973940