Geodesic
Analytic continuation and superconvergence of series of homogeneous polynomials
Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 708-714 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $D$ be a domain in $\mathbb R^n$ ($n\ge1$) and $x^0\in D$. We prove that a necessary and sufficient condition for the existence of a semicontinuous regular method ${\operatorname{A}}$ such that the series expansion of any real-analytic function $f$ in $D$ in homogeneous polynomials around $x^0$ is uniformly summed by this method to $f(x)$ on compact subsets of $D$ is that $D$ be rectilinearly star-shaped with respect to $x^0$. 
@article{MZM_1996_60_5_a5,
     author = {A. V. Pokrovskii},
     title = {Analytic continuation and superconvergence of series of homogeneous polynomials},
     journal = {Matemati\v{c}eskie zametki},
     pages = {708--714},
     year = {1996},
     volume = {60},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a5/}
}
TY  - JOUR
AU  - A. V. Pokrovskii
TI  - Analytic continuation and superconvergence of series of homogeneous polynomials
JO  - Matematičeskie zametki
PY  - 1996
SP  - 708
EP  - 714
VL  - 60
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a5/
LA  - ru
ID  - MZM_1996_60_5_a5
ER  - 
%0 Journal Article
%A A. V. Pokrovskii
%T Analytic continuation and superconvergence of series of homogeneous polynomials
%J Matematičeskie zametki
%D 1996
%P 708-714
%V 60
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a5/
%G ru
%F MZM_1996_60_5_a5
A. V. Pokrovskii. Analytic continuation and superconvergence of series of homogeneous polynomials. Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 708-714. http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a5/

[1] Kuk R., Beskonechnye matritsy i prostranstva posledovatelnostei, Fizmatgiz, M., 1960

[2] Shabat B. V., Vvedenie v kompleksnyi analiz, T. 2, Nauka, M., 1985

[3] Markushevich A. I., “Analiticheskoe prodolzhenie i sverkhskhodimost”, Dokl. AN SSSR, 45:6 (1944), 239–241

[4] Markushevich A. I., Teoriya analiticheskikh funktsii, T. 2, Nauka, M., 1968