Zeros of densities and decomposition problem for multidimensional entire characteristic functions of order 2

Abstract

We consider the entire characteristic functions of order 2 and we prove some decomposition theorems in a multidimensional case. We show that the lack of zeros of the density function is a necessary but not a sufficient (as in the one-dimensional case) condition for a characteristic function to be decomposable. We also find some simple sufficient conditions.

18 pages