Ukrainian Mathematical Journal

, Volume 28, Issue 1, pp 26–30 | Cite as

Inversion of infinite matrices and inefficiency of matrix methods of summation

  • V. I. Mel'nik


Matrix Method Infinite Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    R. G. Cooke, Infinite Matrices and Sequence Spaces, Macmillan, New York (1950).Google Scholar
  2. 2.
    R. Agnew, “Equivalence of methods for evaluation of sequences,” Proe. Amer. Math. Soc.,3, 550–557 (1952).Google Scholar
  3. 3.
    A. Wilansky and K. Zeller, “Summation of bounded divergent sequences, topological methods,” Trans. Amer. Math. Soc.,78, No. 2 (1955).Google Scholar
  4. 4.
    A. Zygmund, Trigonometric Series, Vol. 1, Cambridge Univ. Press (1968).Google Scholar
  5. 5.
    G. A. Mikhalin, “Inefficiency of a class of regular matrices,” Matem. Zametki,16, No. 3 (1974).Google Scholar
  6. 6.
    N. A. Davydov, “Summation of bounded sequences by regular matrices,” Matem. Zametki, 13, No. 2 (1973).Google Scholar
  7. 7.
    A. L. Brudno, “Relative norms of Toeplitz matrices,” Dokl. Akad. Nauk SSSR,91, No. 2 (1953).Google Scholar
  8. 8.
    H. R. Pitt, Tauberian Theorems, Oxford Univ. Press (1958).Google Scholar
  9. 9.
    T. Syrmus, “Some generalizations of a theorem of Mercer,” Uchen. Zap. Tartusk. Gos. Univ.,102 (1961).Google Scholar
  10. 10.
    P. Erdös and G. Piranian, “Laconicity and redundancy of Toeplitz matrices,” Math. Zeit.,83, 381–394 (1964).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • V. I. Mel'nik
    • 1
  1. 1.Kiev Pedagogical InstituteUSSR

Personalised recommendations