A subclass of boundary measures and the convex combination problem for Herglotz-Nevanlinna functions in several variables

TL;DR

This paper explores a specific subclass of boundary measures for Herglotz-Nevanlinna functions in two variables and addresses the convex combination problem for such functions in multiple variables.

Contribution

It introduces a new subclass of boundary measures and provides a solution to the convex combination problem in several variables for Herglotz-Nevanlinna functions.

Findings

Characterization of a particular subclass of boundary measures

Solution to the convex combination problem in multiple variables

Advancement in understanding Herglotz-Nevanlinna functions

Abstract

In this paper, we begin by investigating a particular subclass of boundary measures of Herglotz-Nevanlinna functions in two variables. Based on this, we then proceed to solve the convex combination problem for Herglotz-Nevanlinna functions in several variables.