Plurisubharmonic approximation and boundary values of plurisubharmonic functions
2014 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 413, no 2, 700-714 p.Article in journal (Refereed) Published
We study the problem of approximating plurisubharmonic functions on a bounded domain Omega by continuous plurisubharmonic functions defined on neighborhoods of (Omega) over bar. It turns out that this problem can be linked to the problem of solving a Dirichlet type problem for functions plurisubharmonic on the compact set (Omega) over bar in the sense of Poletsky. A stronger notion of hyperconvexity is introduced to fully utilize this connection, and we show that for this class of domains the duality between the two problems is perfect. In this setting, we give a characterization of plurisubharmonic boundary values, and prove some theorems regarding the approximation of plurisubharmonic functions.
(C) 2013 Elsevier Inc. All rights reserved.
Place, publisher, year, edition, pages
2014. Vol. 413, no 2, 700-714 p.
Plurisubharmonic functions on compacts; Jensen measures; Approximation; Plurisubharmonic extension; Plurisubharmonic boundary values
IdentifiersURN: urn:nbn:se:umu:diva-87147DOI: 10.1016/j.jmaa.2013.12.041ISI: 000331344600014OAI: oai:DiVA.org:umu-87147DiVA: diva2:711792