<p>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 <i>u</i> that is defined on a bounded hyperconvex domain Ω in C<i>n</i><i> </i>and has essentially boundary values zero and bounded Monge-Ampère mass, can be approximated by an increasing sequence of functions {<i>u</i><i>j</i>} 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 C<i>n</i> 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.</p>
| Identifer | oai:union.ndltd.org:UPSALLA/oai:DiVA.org:umu-1799 |
| Date | January 2008 |
| Creators | Hed, Lisa |
| Publisher | Umeå University, Mathematics and Mathematical Statistics, Umeå : Matematik och matematisk statistik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, comprehensive summary, text |
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