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On strong Riesz summability factors of infinite series. I


Author: J. S. Ratti
Journal: Proc. Amer. Math. Soc. 18 (1967), 959-966
MSC: Primary 40.30
DOI: https://doi.org/10.1090/S0002-9939-1967-0218783-3
MathSciNet review: 0218783
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  • D. Borwein and B. L. R. Shawyer, On strong Riesz summability factors, J. London Math. Soc. 40 (1965), 111–126. MR 173885, DOI https://doi.org/10.1112/jlms/s1-40.1.111
  • G. H. Hardy, The second theorem of consistency for summable series, Proc. London Math. Soc. (2) 15 (1916), 72-78. G. H. Hardy and M. Riesz, The general theory of Dirichlet’s series, Cambridge Tracts in Math., No. 18, Cambridge Univ. Press, England. K. A. Hirst, On the second theorem of consistency in the theory of summability by typical means, Proc. London Math. Soc. (2) 33 (1932), 353-366.
  • Pramila Srivastava, On strong Rieszian summability of infinite series, Proc. Nat. Inst. Sci. India Part A 23 (1957), 58–71. MR 96057
  • Pramila Srivastava, On the second theorem of consistency for strong Riesz summability, Indian J. Math. 1 (1958), no. 1, 1–16 (1958). MR 106373
  • J. B. Tatchell, A theorem on absolute Riesz summability, J. London Math. Soc. 29 (1954), 49–59. MR 57993, DOI https://doi.org/10.1112/jlms/s1-29.1.49
  • C. J. de la Vallé-Poussin, Cours d’analyse infinitésimale, Louvain, Paris, 1923.

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Article copyright: © Copyright 1967 American Mathematical Society