Tauberian theorems for generalised Abelian summability methods


STANOJEVIC C., Canak I. , STANOJEVIC V.

7th International Workshop in Analysis and its Applications (IWAA), Orono, Kanada, 1 - 06 Haziran 1997, ss.13-26 identifier

  • Basıldığı Şehir: Orono
  • Basıldığı Ülke: Kanada
  • Sayfa Sayıları: ss.13-26

Özet

Tauberian conditions for the recovery of convergence out of summability, depending on a parameter cease to be Tauberian conditions for some limiting values of the parameter. This situation, motivates the following question. Are there some more general summability methods for which the limiting case would become a Tauberian condition for the behavior of {S-n(a)}? A general summability method is designed whose special cases lead to generalized Abel's summability methods. The Tauberian theorems for those Abel's summability methods contain as a particular case the answer to the above question.