A Tauberian Theorem for Borel-Type Methods of Summability
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 740-747
Voir la notice de l'article provenant de la source Cambridge University Press
Suppose throughout that α >0, β is real, and Nis a non-negative integer such that αN+ β> 0. A series of complex terms is said to be summable (B, α,β) to l if, as x→ ∞, where sn = a 0 + a 1 + ... + an.The Borel-type summability method (B, α, β) is regular, i.e., all convergent series are summable (B, α,β) to their natural sums; and (B,1, 1) is the standard Borel exponential method B.Our aim in this paper is to prove the following Tauberian theorem.THEOREM. Iƒ(i) p ≧ – 1⁄2, an = o(np), and(ii) is summable (B, α,β) to l, then the series is summable by the Cesaro method(C, 2p + 1) to l.
Borwein, D. A Tauberian Theorem for Borel-Type Methods of Summability. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 740-747. doi: 10.4153/CJM-1969-083-7
@article{10_4153_CJM_1969_083_7,
author = {Borwein, D.},
title = {A {Tauberian} {Theorem} for {Borel-Type} {Methods} of {Summability}},
journal = {Canadian journal of mathematics},
pages = {740--747},
year = {1969},
volume = {21},
number = {1},
doi = {10.4153/CJM-1969-083-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-083-7/}
}
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