On approximation by special analytic polyhedral pairs

V. Zahariuta. "On approximation by special analytic polyhedral pairs." Annales Polonici Mathematici 80.1 (2003): 243-256. <http://eudml.org/doc/280575>.

@article{V2003,
abstract = {For bounded logarithmically convex Reinhardt pairs "compact set - domain" (K,D) we solve positively the problem on simultaneous approximation of such a pair by a pair of special analytic polyhedra, generated by the same polynomial mapping f: D → ℂⁿ, n = dimΩ. This problem is closely connected with the problem of approximation of the pluripotential ω(D,K;z) by pluripotentials with a finite set of isolated logarithmic singularities ([23, 24]). The latter problem has been solved recently for arbitrary pluriregular pairs "compact set - domain" (K,D) by Poletsky [12] and S. Nivoche [10, 11], while the first one is still open in the general case.},
author = {V. Zahariuta},
journal = {Annales Polonici Mathematici},
keywords = {pluripotential; Reinhardt domains; special analytic polyhedron},
language = {eng},
number = {1},
pages = {243-256},
title = {On approximation by special analytic polyhedral pairs},
url = {http://eudml.org/doc/280575},
volume = {80},
year = {2003},
}

TY - JOUR
AU - V. Zahariuta
TI - On approximation by special analytic polyhedral pairs
JO - Annales Polonici Mathematici
PY - 2003
VL - 80
IS - 1
SP - 243
EP - 256
AB - For bounded logarithmically convex Reinhardt pairs "compact set - domain" (K,D) we solve positively the problem on simultaneous approximation of such a pair by a pair of special analytic polyhedra, generated by the same polynomial mapping f: D → ℂⁿ, n = dimΩ. This problem is closely connected with the problem of approximation of the pluripotential ω(D,K;z) by pluripotentials with a finite set of isolated logarithmic singularities ([23, 24]). The latter problem has been solved recently for arbitrary pluriregular pairs "compact set - domain" (K,D) by Poletsky [12] and S. Nivoche [10, 11], while the first one is still open in the general case.
LA - eng
KW - pluripotential; Reinhardt domains; special analytic polyhedron
UR - http://eudml.org/doc/280575
ER -