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A property of a class of (¯R, Pn,α) methods for summation of series and Tauberian theorems

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Literature cited

  1. G. H. Hardy, Divergent Series, Oxford Univ. Press (1949).

  2. N. A. Davydov, “On a property of Cesaro methods for summation of series,” Mat. Sb.,38, No. 4, 509–524 (1956).

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  3. G. Polya and G. Szegö, Problems and Theorems in Analysis, Springer-Verlag (1975).

  4. N. A. Davydov, “The (C)-property of Cesaro and Abel-Poisson methods and Tauberian theorems,” Mat. Sb.,60, No. 2, 185–206 (1963).

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Authors and Affiliations

  1. Kiev Pedagogic Institute, USSR

    G. A. Mikhalin & L. S. Teslenko

Authors
  1. G. A. Mikhalin
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  2. L. S. Teslenko
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol, 29, No. 2, pp. 194–203, March–April, 1977.

In conclusion, the authors thank N. A. Davydov for his interest, and V. I. Mel'nik for suggestions enabling the proof of Theorem 1 to be somewhat shortened.

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Mikhalin, G.A., Teslenko, L.S. A property of a class of (¯R, Pn,α) methods for summation of series and Tauberian theorems. Ukr Math J 29, 145–152 (1977). https://doi.org/10.1007/BF01089240

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  • DOI: https://doi.org/10.1007/BF01089240

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