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  • 标题:Some Tauberian theorems for Euler and Borel summability
  • 本地全文:下载
  • 作者:J. A. Fridy ; K. L. Roberts
  • 期刊名称:International Journal of Mathematics and Mathematical Sciences
  • 印刷版ISSN:0161-1712
  • 电子版ISSN:1687-0425
  • 出版年度:1980
  • 卷号:3
  • 期号:4
  • 页码:731-738
  • DOI:10.1155/S0161171280000531
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    The well-known summability methods of Euler and Borel are studied as mappings from ℓ 1 into ℓ 1 . In this ℓ − ℓ setting, the following Tauberian results are proved: if x is a sequence that is mapped into ℓ 1 by the Euler-Knopp method E r with 0$"> r > 0 (or the Borel matrix method) and x satisfies ∑ n = 0 ∞ | x n − x n + 1 | n < ∞ , then x itself is in ℓ 1 .

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