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A new generalization of the Lelong number

Aron Lagerberg (Institutionen för matematiska vetenskaper, matematik)
Arkiv för matematik (0004-2080). Vol. 51 (2013), 1, p. 125-156.
[Artikel, refereegranskad vetenskaplig]

We will introduce a quantity which measures the singularity of a plurisubharmonic function phi relative to another plurisubharmonic function psi, at a point a. We denote this quantity by nu (a,psi) (phi). It can be seen as a generalization of the classical Lelong number in a natural way: if psi=(n-1)log| a <...aEuro parts per thousand a'a|, where n is the dimension of the set where phi is defined, then nu (a,psi) (phi) coincides with the classical Lelong number of phi at the point a. The main theorem of this article says that the upper level sets of our generalized Lelong number, i.e. the sets of the form {z:nu (z,psi) (phi)a parts per thousand yenc} where c > 0, are in fact analytic sets, provided that the weight psi satisfies some additional conditions.

Nyckelord: analyticity, extension

Denna post skapades 2013-04-05. Senast ändrad 2016-11-07.
CPL Pubid: 175361


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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