A Green's function for θ-incomplete polynomials
Joe Callaghan
Annales Polonici Mathematici, Tome 92 (2007), p. 21-35 / Harvested from The Polish Digital Mathematics Library
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Let K be any subset of ℂN. We define a pluricomplex Green’s function VK,θ for θ-incomplete polynomials. We establish properties of VK,θ analogous to those of the weighted pluricomplex Green’s function. When K is a regular compact subset of ℝN, we show that every continuous function that can be approximated uniformly on K by θ-incomplete polynomials, must vanish on K∖supp(ddcVK,θ)N. We prove a version of Siciak’s theorem and a comparison theorem for θ-incomplete polynomials. We compute supp(ddcVK,θ)N when K is a compact section.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:280988 
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     volume = {92},
     year = {2007},
     pages = {21-35},
     zbl = {1124.32015},
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Joe Callaghan. A Green's function for θ-incomplete polynomials. Annales Polonici Mathematici, Tome 92 (2007) pp. 21-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-1-2/