2011•Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)Requires access
Power series with radius of convergence zero — Overconvergence, elongations, summability
Wolfgang Lüh, Arpi A. Stepanyan
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Abstract
We deal with overconvergence phenomena of power series with radius of convergence zero. Among others it is shown that the partial sums of such a series can be elongated to become Cesàro summable on a set S ⊂ { z : | z | > 0} if and only if the considered power series is overconvergent.