About the density of spectral measure of the two-dimensional SaS random vector

Abstract

In this paper, we consider a symmetric α-stable p-sub-stable twodimensional random vector. Our purpose is to show when the function exp − (|a| p + |b| p ) α/p is a characteristic function of such a vector for some p and α. The solution of this problem we can find in [3], in the language of isometric embeddings of Banach spaces. Our proof is based on simple properties of stable distributions and some characterization given in [4].