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Approximation of negative plurisubharmonic functions with given boundary values
Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
Artikel i tidskrift (Refereegranskat) Submitted
Identifikatorer
URN: urn:nbn:se:umu:diva-3346OAI: oai:DiVA.org:umu-3346DiVA, id: diva2:142006
Tillgänglig från: 2008-09-02 Skapad: 2008-09-02Bibliografiskt granskad
Ingår i avhandling
1. Approximation and Subextension of Negative Plurisubharmonic Functions
Öppna denna publikation i ny flik eller fönster >>Approximation and Subextension of Negative Plurisubharmonic Functions
2008 (Engelska)Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Umeå: Matematik och matematisk statistik, 2008. s. 9
Nyckelord
Complex Monge-Ampère operator, Approximation, Plurisubharmonic function, Subextension
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:umu:diva-1799 (URN)978-91-7264-622-3 (ISBN)
Presentation
2008-08-25, N430, Naturvetarhuset, Umeå, 13:15
Opponent
Handledare
Tillgänglig från: 2008-09-02 Skapad: 2008-09-02Bibliografiskt granskad

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