Geodesic
On the interconnection of local and global approximations by holomorphic functions
Izvestiya. Mathematics , Tome 20 (1983) no. 1, pp. 103-118

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

It is proved that if a function $f\in\operatorname{Lip}(\alpha,X)$, $\alpha>2/3$, can be approximated locally outside its zero set by holomorphic functions, then it can be approximated also on the whole compact set $X$. This implies that if $f\in\operatorname{Lip}(\alpha,X)$, $\alpha>2/3$, and $f^2$ can be approximated by holomorphic functions on $X$, then so can $f$. Bibliography: 5 titles. 
@article{IM2_1983_20_1_a6,
     author = {P. V. Paramonov},
     title = {On the interconnection of local and global approximations by holomorphic functions},
     journal = {Izvestiya. Mathematics },
     pages = {103--118},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a6/}
}
TY  - JOUR
AU  - P. V. Paramonov
TI  - On the interconnection of local and global approximations by holomorphic functions
JO  - Izvestiya. Mathematics 
PY  - 1983
SP  - 103
EP  - 118
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a6/
LA  - en
ID  - IM2_1983_20_1_a6
ER  - 
%0 Journal Article
%A P. V. Paramonov
%T On the interconnection of local and global approximations by holomorphic functions
%J Izvestiya. Mathematics 
%D 1983
%P 103-118
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a6/
%G en
%F IM2_1983_20_1_a6
P. V. Paramonov. On the interconnection of local and global approximations by holomorphic functions. Izvestiya. Mathematics , Tome 20 (1983) no. 1, pp. 103-118. http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a6/