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Vinsamlegast notið þetta auðkenni þegar þið vitnið til verksins eða tengið í það: http://hdl.handle.net/1946/4137

Titill: 
  • Pluricomplex Green Functions with Logarithmic Poles at Infinity
Námsstig: 
  • Meistara
Leiðbeinandi: 
Útdráttur: 
  • In this thesis we study the pluricomplex Green function with logarithmic poles at
    infinity, V_{X,q}, for a subset X of C^n and a weight function q on X. We study
    the continuity properties of V_{X,q} with respect to X and q. If K is compact and q
    continuous we show that V_{K,q} coincides with log Φ_{K,q}, where Φ_{K,q} is Siciak's extremal function.
    We prove Siciak's approximation theorem for holomorphic functions, which gives
    a necessary and sufficient condition for a holomorphic function to have a holomorphic
    extension to a sublevel set of the Green function and the largest sublevel set where
    an extension exists.
    A proof of a disc formula for the Green function is presented when X is an open
    domain and q upper semicontinuous. This allow us to evaluate the Green function
    using analytic discs in the complex projective space P^n .

Styrktaraðili: 
  • Rannsóknarnámssjóður Rannís, Rannsóknasjóður Háskóla Íslands
Samþykkt: 
  • 18.5.2007
URI: 
  • http://hdl.handle.net/1946/4137


Skrár
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Pluricomplex_Green_Functions_fixed.pdf519.59 kBOpinnHeildartextiPDFSkoða/Opna