Geodesic
An estimate for polynomials on analytic sets
Izvestiya. Mathematics , Tome 20 (1983) no. 3, pp. 493-502

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $A$ be a connected, analytic (in general, not closed) subset of the complex space $\mathbf C^n$ and let $K\subset A$ be a compact set which is not pluri-polar in $A$. In this article it is proved that the extremal function $V(z,K)$ is locally bounded on $A$ if and only if $A$ belongs to some algebraic set of the same dimension as $A$. Moreover, it is shown that for an algebraic set $A$ in a neighborhood of any ordinary point $z^0\in A_0$ the function $V(z,K)$ can be represented as the limit of an increasing sequence of maximal functions. Bibliography: 10 titles. 
@article{IM2_1983_20_3_a4,
     author = {A. S. Sadullaev},
     title = {An estimate for polynomials on analytic sets},
     journal = {Izvestiya. Mathematics },
     pages = {493--502},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1983_20_3_a4/}
}
TY  - JOUR
AU  - A. S. Sadullaev
TI  - An estimate for polynomials on analytic sets
JO  - Izvestiya. Mathematics 
PY  - 1983
SP  - 493
EP  - 502
VL  - 20
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1983_20_3_a4/
LA  - en
ID  - IM2_1983_20_3_a4
ER  - 
%0 Journal Article
%A A. S. Sadullaev
%T An estimate for polynomials on analytic sets
%J Izvestiya. Mathematics 
%D 1983
%P 493-502
%V 20
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1983_20_3_a4/
%G en
%F IM2_1983_20_3_a4
A. S. Sadullaev. An estimate for polynomials on analytic sets. Izvestiya. Mathematics , Tome 20 (1983) no. 3, pp. 493-502. http://geodesic.mathdoc.fr/item/IM2_1983_20_3_a4/