Geodesic
Conditions for the representability of analytic functions by series of rational functions
Matematičeskie zametki, Tome 15 (1974) no. 2, pp. 197-203 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

With a function $f(z)$, analytic in the unit circle, we associate by a specific rule the series $\sum_{n=1}^\infty\frac{A_n}{a-\lambda_nz}$, $|\lambda_n|<1$. We derive a (necessary and sufficient) condition for the convergence of the series in the unit circle. We derive further conditions under which the series converges to the function $f(z)$ itself. 
@article{MZM_1974_15_2_a2,
     author = {T. A. Leont'eva},
     title = {Conditions for the representability of analytic functions by series of rational functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {197--203},
     year = {1974},
     volume = {15},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_2_a2/}
}
TY  - JOUR
AU  - T. A. Leont'eva
TI  - Conditions for the representability of analytic functions by series of rational functions
JO  - Matematičeskie zametki
PY  - 1974
SP  - 197
EP  - 203
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_1974_15_2_a2/
LA  - ru
ID  - MZM_1974_15_2_a2
ER  - 
%0 Journal Article
%A T. A. Leont'eva
%T Conditions for the representability of analytic functions by series of rational functions
%J Matematičeskie zametki
%D 1974
%P 197-203
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1974_15_2_a2/
%G ru
%F MZM_1974_15_2_a2
T. A. Leont'eva. Conditions for the representability of analytic functions by series of rational functions. Matematičeskie zametki, Tome 15 (1974) no. 2, pp. 197-203. http://geodesic.mathdoc.fr/item/MZM_1974_15_2_a2/