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Approximation and Subextension of Negative Plurisubharmonic Functions
Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
2008 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
Umeå: Matematik och matematisk statistik , 2008. , s. 9
Emneord [en]
Complex Monge-Ampère operator, Approximation, Plurisubharmonic function, Subextension
HSV kategori
Identifikatorer
URN: urn:nbn:se:umu:diva-1799ISBN: 978-91-7264-622-3 (tryckt)OAI: oai:DiVA.org:umu-1799DiVA, id: diva2:142007
Presentation
2008-08-25, N430, Naturvetarhuset, Umeå, 13:15
Opponent
Veileder
Tilgjengelig fra: 2008-09-02 Laget: 2008-09-02bibliografisk kontrollert
Delarbeid
1. Subextension and approximation of negative plurisubharmonic functions
Åpne denne publikasjonen i ny fane eller vindu >>Subextension and approximation of negative plurisubharmonic functions
2008 (engelsk)Inngår i: The Michigan mathematical journal, ISSN 0026-2285, E-ISSN 1945-2365, Vol. 56, s. 593-601Artikkel i tidsskrift (Fagfellevurdert) Published
Identifikatorer
urn:nbn:se:umu:diva-3344 (URN)
Tilgjengelig fra: 2008-09-02 Laget: 2008-09-02 Sist oppdatert: 2018-06-09bibliografisk kontrollert
2. Subextension of plurisubharmonic functions without increasing the total Monge-Ampère mass
Åpne denne publikasjonen i ny fane eller vindu >>Subextension of plurisubharmonic functions without increasing the total Monge-Ampère mass
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
Identifikatorer
urn:nbn:se:umu:diva-3345 (URN)
Tilgjengelig fra: 2008-09-02 Laget: 2008-09-02 Sist oppdatert: 2022-05-10
3. Approximation of negative plurisubharmonic functions with given boundary values
Åpne denne publikasjonen i ny fane eller vindu >>Approximation of negative plurisubharmonic functions with given boundary values
2010 (engelsk)Inngår i: International Journal of Mathematics, ISSN 0129-167X, Vol. 21, nr 9, s. 1135-1145Artikkel i tidsskrift (Fagfellevurdert) 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.

Emneord
Complex Monge-Ampere operator, approximation, subextension, plurisubharmonic function
HSV kategori
Identifikatorer
urn:nbn:se:umu:diva-3346 (URN)10.1142/S0129167X10006410 (DOI)000282021300003 ()2-s2.0-77956915137 (Scopus ID)
Merknad

Previously included in thesis in manuscript form. 

Tilgjengelig fra: 2008-09-02 Laget: 2008-09-02 Sist oppdatert: 2023-03-24bibliografisk kontrollert

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