Acta Mathematica Hungarica

, Volume 45, Issue 1–2, pp 151–158 | Cite as

Conditions for inclusion between Nörlund summability methods

  • D. Borwein
  • B. Thorpe
Article

Keywords

Summability Method 

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References

  1. [1]
    A. F. Andersen, Comparison theorems in the theory of Cesàro summability,Proc. Lond. Math. Soc.,27 (1928), 39–71.Google Scholar
  2. [2]
    G. H. Hardy,Divergent Series (Oxford, 1949).Google Scholar
  3. [3]
    G. H. Hardy and J. E. Littlewood, Solution of the Cesàro summability problem for power series and Fourier series,Math. Zeit.,19 (1924), 67–96.Google Scholar
  4. [4]
    J. D. Hill, On perfect methods of summability,Duke Math. J.,3 (1937), 702–714.Google Scholar
  5. [5]
    E. Kogbetliantz, Sommation des séries et integrales divergentes par les moyennes arithmétiques et typiques,Mémorial des sciences mathématiques, No. 51 (Paris, 1931).Google Scholar
  6. [6]
    J. E. Littlewood,Lectures on the Theory of Functions (Oxford, 1943).Google Scholar
  7. [7]
    W. Miesner, The convergence fields of Nörlund means,Proc. Lond. Math. Soc.,15 (1965), 495–507.Google Scholar
  8. [8]
    G. Petersen, A note on divergent series,Canad. J. Math. 4 (1952), 445–454.Google Scholar
  9. [9]
    A. Peyerimhoff,Lectures on Summability, Springer Lecture Notes, No. 107 (Berlin).Google Scholar
  10. [10]
    G. Szegö,Orthogonal Polynomials, Amer. Math. Soc. Colloquium Publication, Vol. 23 (New York, 1939).Google Scholar
  11. [11]
    C. E. Winn, On strong summability for any positive order,Math. Zeit.,37 (1933), 481–492.Google Scholar
  12. [12]
    A. Zygmund,Trigonometric Series (Cambridge, 1959).Google Scholar

Copyright information

© Akadémiai Kiadó 1985

Authors and Affiliations

  • D. Borwein
    • 1
  • B. Thorpe
    • 1
  1. 1.The University of Western OntarioLondonCanada

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