This article is cited in 1 paper

Analytic continuation and superconvergence of series of homogeneous polynomials

A. V. Pokrovskii

M. V. Lomonosov Moscow State University

Abstract: 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 $x^0$.

UDC: 517.5

Received: 03.10.1994
Revised: 03.11.1995

DOI: 10.4213/mzm1883

 English version: Mathematical Notes, 1996, 60:5, 531–535

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