Rational approximation and pluripolar sets

A. S. Sadullaev

Sbornik. Mathematics, Tome 47 (1984) no. 1, pp. 91-113

Résumé

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.

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