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Tauberian relations between the Abel-type and the Borel-type methods of summability

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Abstract

We consider the conditions underwhich a series, summable by an Abel-type method, is also summable by a Borel-type method. This extends and improves the known result of G. Doetsch.

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Authors and Affiliations

  1. Department of Mathematics, University of Western Ontario, London 72, Ontario, Canada

    Bruce L. R. Shawyer

  2. Department of Mathematics, National Tsing Hua University, Kuang Fu Road, Hsinchu, Taiwan, China

    G. S. Yang

Authors
  1. Bruce L. R. Shawyer
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  2. G. S. Yang
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Supported in part by the National Research Council of Canada.

Supported in part by the Mathematics Research Center, National Science Council, Taiwan, Republic of China.

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Shawyer, B.L.R., Yang, G.S. Tauberian relations between the Abel-type and the Borel-type methods of summability. Manuscripta Math 5, 341–357 (1971). https://doi.org/10.1007/BF01367769

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  • DOI: https://doi.org/10.1007/BF01367769

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