Extension and 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.

Cited by in corpus (2)

• The classification of holomorphic $(m,n)$--subharmonic morphisms
• Approximation of $m-$subharmonic functions on bounded domains in ${\mathbb{C}}^n$