Matematičeskie zametki, Tome 15 (1974) no. 2, pp. 197-203
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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/
@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
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.
