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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-22,
author = {V. Zahariuta},
title = {On approximation by special analytic polyhedral pairs},
journal = {Annales Polonici Mathematici},
volume = {81},
year = {2003},
pages = {243-256},
zbl = {1026.32002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-22}
}
V. Zahariuta. On approximation by special analytic polyhedral pairs. Annales Polonici Mathematici, Tome 81 (2003) pp. 243-256. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-22/