# On properties of Bernstein functions of several complex variables

## TL;DR

This paper extends Bernstein functions to multiple complex variables, providing new proofs and examples to deepen understanding of their properties in higher dimensions.

## Contribution

It introduces a multidimensional Bernstein class, offers a new proof of their integral representation, and explores their properties through examples.

## Key findings

- Established a multidimensional Bernstein class
- Provided a new proof of integral representation
- Presented illustrative examples

## Abstract

A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables is given. Examples are considered.