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Plurisubharmonic approximation and boundary values of plurisubharmonic functions
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
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
Abstract [en]

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.

Place, publisher, year, edition, pages
2014. Vol. 413, no 2, 700-714 p.
Keyword [en]
Plurisubharmonic functions on compacts, Jensen measures, Approximation, Plurisubharmonic extension, Plurisubharmonic boundary values
National Category
URN: urn:nbn:se:uu:diva-220970DOI: 10.1016/j.jmaa.2013.12.041ISI: 000331344600014OAI: oai:DiVA.org:uu-220970DiVA: diva2:707923
Available from: 2014-03-26 Created: 2014-03-24 Last updated: 2015-04-16Bibliographically approved

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Persson, Håkan
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