Rational approximation and pluripolar sets
Sbornik. Mathematics, Tome 47 (1984) no. 1, pp. 91-113
Voir la notice de l'article provenant de la source Math-Net.Ru
The main result in the article is
Theorem. Let $S\subset\mathbf C^n$ be a closed set such that $0\notin S$ and $\mathbf C^n\setminus S$ is a pseudoconvex domain. If for almost every complex line $l$ passing through $0$ the intersection $l\cap S$ is polar in $l$, then $S$ is a pluripolar set in $\mathbf C^n$.
This theorem is then applied to the analysis of sets of singularities of holomorphic functions which are rapidly approximated by rational functions.
Bibliography: 21 titles.
@article{SM_1984_47_1_a5,
author = {A. S. Sadullaev},
title = {Rational approximation and pluripolar sets},
journal = {Sbornik. Mathematics},
pages = {91--113},
publisher = {mathdoc},
volume = {47},
number = {1},
year = {1984},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1984_47_1_a5/}
}
A. S. Sadullaev. Rational approximation and pluripolar sets. Sbornik. Mathematics, Tome 47 (1984) no. 1, pp. 91-113. http://geodesic.mathdoc.fr/item/SM_1984_47_1_a5/