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On boundary values of plurisubharmonic functions
Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
Abstract [en]

In this paper we describe how boundary values of bounded plurisubharmonic functions can be defined in terms of measures with support on the boundary. We do this by approximating the boundary measures with measures on the interior of the domain, and present conditions on the approximation which makes the procedure suitable for defining boundary values of certain plurisubharmonic functions.

Nyckelord [en]
plurisubharmonic functions, boundary values
Nationell ämneskategori
Matematisk analys
Forskningsämne
matematik
Identifikatorer
URN: urn:nbn:se:umu:diva-27777OAI: oai:DiVA.org:umu-27777DiVA, id: diva2:277583
Projekt
plurisubharmonic functions, boundary valuesTillgänglig från: 2009-11-24 Skapad: 2009-11-19 Senast uppdaterad: 2018-06-08Bibliografiskt granskad
Ingår i avhandling
1. Boundary values of plurisubharmonic functions and related topics
Öppna denna publikation i ny flik eller fönster >>Boundary values of plurisubharmonic functions and related topics
2009 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

This thesis consists of three papers concerning problems related to plurisubharmonic functions on bounded hyperconvex domains, in particular boundary values of such functions. The papers summarized in this thesis are:* Paper I Urban Cegrell and Berit Kemppe, Monge-Ampère boundary measures, Ann. Polon. Math. 96 (2009), 175-196.* Paper II Berit Kemppe, An ordering of measures induced by plurisubharmonic functions, manuscript (2009).* Paper III Berit Kemppe, On boundary values of plurisubharmonic functions, manuscript (2009).In the first paper we study a procedure for sweeping out Monge-Ampère measures to the boundary of the domain. The boundary measures thus obtained generalize measures studied by Demailly. A number of properties of the boundary measures are proved, and we describe how boundary values of bounded plurisubharmonic functions can be associated to the boundary measures.In the second paper, we study an ordering of measures induced by plurisubharmonic functions. This ordering arises naturally in connection with problems related to negative plurisubharmonic functions. We study maximality with respect to the ordering and a related notion of minimality for certain plurisubharmonic functions. The ordering is then applied to problems of weak*-convergence of measures, in particular Monge-Ampère measures.In the third paper we continue the work on boundary values in a more general setting than in Paper I. We approximate measures living on the boundary with measures on the interior of the domain, and present conditions on the approximation which makes the procedure suitable for defining boundary values of certain plurisubharmonic functions.

Ort, förlag, år, upplaga, sidor
Umeå: Umeå University, Department of Mathematics, 2009
Serie
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 43
Nyckelord
Plurisubharmonic functions, boundary measures, boundary values, complex Monge-Ampère operator, weak*-convergence
Nationell ämneskategori
Matematisk analys
Forskningsämne
matematik
Identifikatorer
urn:nbn:se:umu:diva-29870 (URN)978-91-7264-906-4 (ISBN)
Disputation
2009-12-18, MA121, MIT-huset, Umeå universitet, 901 87 Umeå, Umeå, 10:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2009-11-27 Skapad: 2009-11-25 Senast uppdaterad: 2018-06-08Bibliografiskt granskad

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