A Green's function for θ-incomplete polynomials

Joe Callaghan. "A Green's function for θ-incomplete polynomials." Annales Polonici Mathematici 90.1 (2007): 21-35. <http://eudml.org/doc/280988>.

@article{JoeCallaghan2007,
abstract = {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.},
author = {Joe Callaghan},
journal = {Annales Polonici Mathematici},
keywords = {pluricomplex Green function; weighted pluripotential theory; incomplete polynomials},
language = {eng},
number = {1},
pages = {21-35},
title = {A Green's function for θ-incomplete polynomials},
url = {http://eudml.org/doc/280988},
volume = {90},
year = {2007},
}

TY - JOUR
AU - Joe Callaghan
TI - A Green's function for θ-incomplete polynomials
JO - Annales Polonici Mathematici
PY - 2007
VL - 90
IS - 1
SP - 21
EP - 35
AB - 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.
LA - eng
KW - pluricomplex Green function; weighted pluripotential theory; incomplete polynomials
UR - http://eudml.org/doc/280988
ER -