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A Green's function for θ-incomplete polynomials

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Callaghan J.

Annales Polonici Mathematici

2007

tom 90

nr 1

21-35

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.

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1 Annales Polonici Mathematici

1 Callaghan J.

1 2007

Wyniki wyszukiwania

A Green's function for θ-incomplete polynomials