Geodesic
Analytic continuation and superconvergence of series of homogeneous polynomials
Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 708-714.

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

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 $x^0$. 
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     author = {A. V. Pokrovskii},
     title = {Analytic continuation and superconvergence of series of homogeneous polynomials},
     journal = {Matemati\v{c}eskie zametki},
     pages = {708--714},
     publisher = {mathdoc},
     volume = {60},
     number = {5},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a5/}
}
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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/

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