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Approximation of negative plurisubharmonic functions with given boundary values
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2010 (English)In: International Journal of Mathematics, ISSN 0129-167X, Vol. 21, no 9, p. 1135-1145Article in journal (Refereed) Published
Abstract [en]

In this paper, we study the approximation of negative plurisubharmonic functions with given boundary values. We want to approximate a plurisubharmonic function by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.

Place, publisher, year, edition, pages
2010. Vol. 21, no 9, p. 1135-1145
Keywords [en]
Complex Monge-Ampere operator, approximation, subextension, plurisubharmonic function
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-3346DOI: 10.1142/S0129167X10006410ISI: 000282021300003Scopus ID: 2-s2.0-77956915137OAI: oai:DiVA.org:umu-3346DiVA, id: diva2:142006
Note

Previously included in thesis in manuscript form. 

Available from: 2008-09-02 Created: 2008-09-02 Last updated: 2023-03-24Bibliographically approved
In thesis
1. Approximation and Subextension of Negative Plurisubharmonic Functions
Open this publication in new window or tab >>Approximation and Subextension of Negative Plurisubharmonic Functions
2008 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we study approximation of negative plurisubharmonic functions by functions defined on strictly larger domains. We show that, under certain conditions, every function u that is defined on a bounded hyperconvex domain Ω in Cn and has essentially boundary values zero and bounded Monge-Ampère mass, can be approximated by an increasing sequence of functions {uj} that are defined on strictly larger domains, has boundary values zero and bounded Monge-Ampère mass. We also generalize this and show that, under the same conditions, the approximation property is true if the function u has essentially boundary values G, where G is a plurisubharmonic functions with certain properties. To show these approximation theorems we use subextension. We show that if Ω_1 and Ω_2 are hyperconvex domains in Cn and if u is a plurisubharmonic function on Ω_1 with given boundary values and with bounded Monge-Ampère mass, then we can find a plurisubharmonic function û defined on Ω_2, with given boundary values, such that û <= u on Ω and with control over the Monge-Ampère mass of û.

Place, publisher, year, edition, pages
Umeå: Matematik och matematisk statistik, 2008. p. 9
Keywords
Complex Monge-Ampère operator, Approximation, Plurisubharmonic function, Subextension
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-1799 (URN)978-91-7264-622-3 (ISBN)
Presentation
2008-08-25, N430, Naturvetarhuset, Umeå, 13:15
Opponent
Supervisors
Available from: 2008-09-02 Created: 2008-09-02Bibliographically approved

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Hed, Lisa

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