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

TL;DR

This paper investigates the properties of multidimensional entire characteristic functions of order 2, establishing decomposition theorems and conditions related to the zeros of their density functions.

Contribution

It extends decomposition theorems to multidimensional cases and clarifies the role of zeros in density functions for characteristic function decomposability.

Findings

Lack of zeros in the density function is necessary but not sufficient for decomposability.

Provides simple sufficient conditions for decomposability.

Extends one-dimensional decomposition results to multidimensional settings.

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.