# Extension and approximation of $m$-subharmonic functions

## TL;DR

This paper characterizes which boundary functions on a domain can be extended inward as $m$-subharmonic functions, using algebraic methods and focusing on approximation and extension properties of these functions.

## Contribution

It provides a new characterization of boundary functions extendable as $m$-subharmonic functions via an algebraic approach and discusses approximation techniques.

## Key findings

- Characterization of boundary functions extendable as $m$-subharmonic functions.
- Use of algebraic methods to analyze $m$-subharmonic functions on compact sets.
- Remarks on approximation of $m$-subharmonic functions.

## Abstract

Let $\Omega\subset \mathbb C^n$ be a bounded domain, and let $f$ be a real-valued function defined on the whole topological boundary $\partial \Omega$. The aim of this paper is to find a characterization of the functions $f$ which can be extended to the inside to a $m$-subharmonic function under suitable assumptions on $\Omega$. We shall do so by using a function algebraic approach with focus on $m$-subharmonic functions defined on compact sets. We end this note with some remarks on approximation of $m$-subharmonic functions.