A Green's function for θ-incomplete polynomials

• Autorzy: Joe Callaghan
• Języki publikacji: EN

Abstrakty

EN

Let K be any subset of $ℂ^N$. We define a pluricomplex Green's function $V_{K,θ}$ for θ-incomplete polynomials. We establish properties of $V_{K,θ}$ analogous to those of the weighted pluricomplex Green's function. When K is a regular compact subset of $ℝ^N$, we show that every continuous function that can be approximated uniformly on K by θ-incomplete polynomials, must vanish on $K∖supp(dd^{c} V_{K,θ})^N$. We prove a version of Siciak's theorem and a comparison theorem for θ-incomplete polynomials. We compute $supp(dd^{c} V_{K,θ})^N$ when K is a compact section.

Kategorie tematyczne

• 32U35: Pluricomplex Green functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2007
• Tom: 90
• Numer: 1
• Strony: 21-35

Daty

wydano

2007

Twórcy

autor

Joe Callaghan

• Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 2E4, Canada

Identyfikatory

DOI

10.4064/ap90-1-2