Some Tauberian theorems for Euler and Borel summability

J. A. Fridy and K. L. Roberts

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-8

Abstract:

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 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 .

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:276340

DOI: 10.1155/S0161171280000531

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