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Göteborgs universitets publikationer

Bergman kernels for weighted polynomials and weighted equilibrium measures of C^n

Författare och institution:
Robert Berman (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
Indiana University Mathematics Journal, 58 ( 4 ) s. 1921-1946
ISSN:
0022-2518
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2009
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in \C^{n} of total degree at most k, equipped with a weighted norm, are obtained. The weight function is assumed to be C^{1,1}, i.e. it is differentiable and all of its first partial derivatives are locally Lipshitz continuous. The convergence is studied in the large k limit and is expressed in terms of the global equilibrium potential associated to the weight function, as well as in terms of the Monge-Ampere measure of the weight function itself on a certain set. A setting of polynomials associated to a given Newton polytope, scaled by k, is also considered. These results apply directly to the study of the distribution of zeroes of random polynomials and of the eigenvalues of random normal matrices.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Postens nummer:
113195
Posten skapad:
2010-02-19 13:04
Posten ändrad:
2016-08-16 10:22

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