Approximation of plurisubharmonic functions on bounded domains in \(\mathbb C^n\)
Let \(\Omega\) be a domain in \(\mathbb{C}^n\) and \(PSH^- (\Omega)\) be the set of plurisubharmonic functions bounded from above on \(\Omega.\) The main results of this paper are the following facts. {\parindent6mm \begin{itemize}\item[(1)] In Theorem 3.2 it is established when every \(u \in PSH^- (\Omega)\) is the pointwise limit of a sequence \(\{u_j\}\) of smooth plurisubharmonic functions on neighborhood of \(\overline {\Omega}\). Moreover, it is shown that if \(u\) is locally bounded on \(\Omega\), then \(\{u_j\}\) can be chosen such that \[ (d d^c u_j)^n \to (d d^c u)^n \] in the sense of currents. \item[(2)] In Theorem 4.4, a condition for \(\Omega\) so Theorem 3.2 will be valid is given. \end{itemize}}
scientific article; zbMATH DE number 5373799