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Abstract

In this paper we obtain the necessary and sufficient conditions on permutations of numerical series which transformed any B-summable series into an A-summable series, where A and B are matrices satisfying certain conditions.

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Literature cited

  1. E. Borel, “Sur le changement de l'ordre des termes d'une serie semiconvergente,” Bull. Sci. Math., (2),14, 97 (1890).

    Google Scholar 

  2. F. W. Levi, “Rearrangement of convergent series,” Duke Math. J.,13, 579–585 (1946).

    Google Scholar 

  3. R. P. Agnew, “Permutations preserving convergence of series,” Proc. Amer. Math. Soc.,6, 563–564 (1955).

    Google Scholar 

  4. N. Bourbaki, Topologie Générale, 2m ed., Paris (1951).

  5. A. S. Kronrod, “The rearrangement of the terms of numerical series,” Matem. Sb.,18(60), No. 2, 237–280 (1946).

    Google Scholar 

  6. A. Robertson, “On the rearrangement of infinite series,” Proc. Glasgow Math. Assoc.,3, 182–193 (1958).

    Google Scholar 

  7. G. H. Hardy, Divergent Series, Oxford University Press.

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Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 13–20, January, 1973.

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Sabo, D. Rearrangements of summable numerical series. Mathematical Notes of the Academy of Sciences of the USSR 13, 9–13 (1973). https://doi.org/10.1007/BF01093621

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  • DOI: https://doi.org/10.1007/BF01093621

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