Geodesic
A~boundary uniqueness theorem in~$\mathbf C^n$
Sbornik. Mathematics, Tome 30 (1976) no. 4, pp. 501-514

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

The classical boundary theorem of F. and M. Riesz asserts that, if the radial limits of a bounded holomorphic function $f(z)$ in the disk $|z|1$ lie in a set of capacity zero for a set of positive measure on the circle $|z|=1$, then $f(z)\equiv\mathrm{constant}$. The main result of this paper is the proof of an analogous theorem for maps $F\colon D\to\mathbf C^n$, where $D$ is a domain in $\mathbf C^n$. We take as uniqueness set on the boundary any set of positive Lebesgue measure on a generating submanifold. Bibliography: 12 titles. 
@article{SM_1976_30_4_a4,
     author = {A. S. Sadullaev},
     title = {A~boundary uniqueness theorem in~$\mathbf C^n$},
     journal = {Sbornik. Mathematics},
     pages = {501--514},
     publisher = {mathdoc},
     volume = {30},
     number = {4},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_30_4_a4/}
}
TY  - JOUR
AU  - A. S. Sadullaev
TI  - A~boundary uniqueness theorem in~$\mathbf C^n$
JO  - Sbornik. Mathematics
PY  - 1976
SP  - 501
EP  - 514
VL  - 30
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1976_30_4_a4/
LA  - en
ID  - SM_1976_30_4_a4
ER  - 
%0 Journal Article
%A A. S. Sadullaev
%T A~boundary uniqueness theorem in~$\mathbf C^n$
%J Sbornik. Mathematics
%D 1976
%P 501-514
%V 30
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1976_30_4_a4/
%G en
%F SM_1976_30_4_a4
A. S. Sadullaev. A~boundary uniqueness theorem in~$\mathbf C^n$. Sbornik. Mathematics, Tome 30 (1976) no. 4, pp. 501-514. http://geodesic.mathdoc.fr/item/SM_1976_30_4_a4/