Computational Methods and Function Theory 2 (2002), No. 1, 137--153
Copyright Heldermann Verlag 2002
Norair Arakelian
arakelian@instmath.sci.am, Institute of Mathematics NAS of Armenia, Bagramian 24b, 375019 Yerevan, Armenia.
Wolfgang Luh
luh@uni-trier.de, Universität Trier, Fachbereich Mathematik, D-54286 Trier, Germany.
In this paper we discuss some problems on efficient analytic continuation of power series in the complex plane by means of summability methods, given by ``universal'' matrices. First, we present a new class of sets differing from domains, allowing efficient summation by those methods; after that, we establish the existence of those methods for the\ local restoration of the analytic continuation of power series in arbitrary domains.
Keywords: Analytic element, analytic continuation, matrix summation.
MSC 2000: Primary 30B40; Secondary 40C05.
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