- 期刊
SOME TAUBERIAN THEORENS FOR EULER AND BOREL SUMMABILITY
並列摘要
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 r ＞ 0 (or the Borel matrix method) and x satisfies Σ_(n=0)^∞|x_n-X_(n+1)|√n ＜ ∞, then x itself is in l^1.
延伸閱讀
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- CAMPBELL, G. B. (1994). A NEW CLASS OF INFINITE PRODUCTS, AND EULER'S TOTIENT. International Journal of Mathematics and Mathematical Sciences, 1994(), 417-422. https://doi.org/10.1155/S0161171294000591
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- CHUN, C., & FREEDMAN, A. (1989). A BOUNDED CONSISTENCY THEOREM FOR STRONG SUMMABILITIES. International Journal of Mathematics and Mathematical Sciences, 1989(), 39-46. https://doi.org/10.1155/S0161171289000050