Geodesic
Pointwise and locally uniform convergence of holomorphic and harmonic functions
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 665-678.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We shall characterize the sets of locally uniform convergence of pointwise convergent sequences. Results obtained for sequences of holomorphic functions by Hartogs and Rosenthal in 1928 will be generalized for many other sheaves of functions. In particular, our Hartogs-Rosenthal type theorem holds for the sheaf of solutions to the second order elliptic PDE's as well as it has applications to the theory of harmonic spaces.
Classification : 30E10, 31B05, 31D05, 35J15, 35J99
Keywords: Osgood's theorem; approximation; maximum principle; harmonic space; elliptic PDE's 
@article{CMUC_1999__40_4_a5,
     author = {\v{S}t\v{e}pni\v{c}kov\'a, Libu\v{s}e},
     title = {Pointwise and locally uniform convergence of holomorphic and harmonic functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {665--678},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {1999},
     mrnumber = {1756543},
     zbl = {1009.31002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1999__40_4_a5/}
}
TY  - JOUR
AU  - Štěpničková, Libuše
TI  - Pointwise and locally uniform convergence of holomorphic and harmonic functions
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1999
SP  - 665
EP  - 678
VL  - 40
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1999__40_4_a5/
LA  - en
ID  - CMUC_1999__40_4_a5
ER  - 
%0 Journal Article
%A Štěpničková, Libuše
%T Pointwise and locally uniform convergence of holomorphic and harmonic functions
%J Commentationes Mathematicae Universitatis Carolinae
%D 1999
%P 665-678
%V 40
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1999__40_4_a5/
%G en
%F CMUC_1999__40_4_a5
Štěpničková, Libuše. Pointwise and locally uniform convergence of holomorphic and harmonic functions. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 665-678. http://geodesic.mathdoc.fr/item/CMUC_1999__40_4_a5/