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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Overconvergence and $(C, 1)$ summability


Author: Vladimir Drobot
Journal: Proc. Amer. Math. Soc. 25 (1970), 13-15
MSC: Primary 30.21
DOI: https://doi.org/10.1090/S0002-9939-1970-0254220-0
MathSciNet review: 0254220
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that a power series can be diluted to become $(C,1)$ summable outside the radius of convergence if and only if it overconverges.


References [Enhancements On Off] (What's this?)

  • G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
  • S. Mazur, Conditionally convergent series, Soc. Sav. Sci. Lett. Lwow. 4 (1929), 411-424.

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Additional Information

Keywords: Dilution of series, <IMG WIDTH="55" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$(C,1)$"> summability, overconvergence of power series
Article copyright: © Copyright 1970 American Mathematical Society