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An extension of Mercer's theorem


Authors: R. T. Leslie and E. R. Love
Journal: Proc. Amer. Math. Soc. 3 (1952), 448-457
MSC: Primary 40.0X
DOI: https://doi.org/10.1090/S0002-9939-1952-0047159-6
MathSciNet review: 0047159
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  • [4] E. T. Copson and W. L. Ferrar, Notes on the structure of sequences, J. London, Math. Soc. vol. 4 (1929) pp. 258-264 and vol. 5 (1930) pp. 21-27.
  • [5] Wallie Abraham Hurwitz, The Oscillation of a Sequence, Amer. J. Math. 52 (1930), no. 3, 611–616. MR 1506778, https://doi.org/10.2307/2370629
  • [6] R. P. Agnew, On equivalence of methods of evaluation of sequences, Tôhoku Math. J. vol. 35 (1932) pp. 244-252.
  • [7] J. Karamata, Sur quelques inversions d'une proposition de Cauchy, Tôhoku Math. J. vol. 36 (1933) pp. 22-28.
  • [8] H. R. Pitt, Mercerian theorems, Proc. Cambridge Philos. Soc. vol. 34 (1938) pp. 510-520.
  • [9] W. W. Rogosinski, On Hausdorff’s methods of summability, Proc. Cambridge Philos. Soc. 38 (1942), 166–192. MR 0006380
  • [10] G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
  • [11] E. R. Love, Mercer's summability theorem, accepted for publication in J. London Math. Soc.

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DOI: https://doi.org/10.1090/S0002-9939-1952-0047159-6
Article copyright: © Copyright 1952 American Mathematical Society