Geodesic
On Strong Nörlund Summability Fields
Canadian journal of mathematics, Tome 24 (1972) no. 3, pp. 390-399

Voir la notice de l'article provenant de la source Cambridge University Press

Let p denote the sequence {pn} and set wherever this series converges. (Where no limits are stated, sums are throughout to be taken from n = 0 to n = ∞.) We use a similar notation with other letters in place of p. Given two sequences p, q, the convolution p*q is defined by it is familiar, and easily verified, that the operation of convolution is commutative and associative. We write Pn = (p*l)n (where 1 denotes the sequence {1} ), and take P-1 to mean 0. If, for all n ≦ 0, Pn ≠ 0, then we define the Nörlund mean (N, p) of the sequence s as σn, where and (σ-1 = 0. If σn → λ as n → ∞, then 5 is said to be limitable (N, p) to the number λ 
Kuttner, Brian; Thorpe, Brian. On Strong Nörlund Summability Fields. Canadian journal of mathematics, Tome 24 (1972) no. 3, pp. 390-399. doi: 10.4153/CJM-1972-032-4
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[1] 1. Borwein, D. and Cass, F. P., Strong Nörland summability, Math. Z. 103 (1968), 94–111. Google Scholar

[2] 2. Hardy, G. H., Divergent series (Oxford University Press, London, 1949). Google Scholar

[3] 3. Kuttner, B. and Thorpe, B., On the strong Nörlund summability of a Cauchy product series, Math. Z. 111 (1969), 69–86. Google Scholar

[4] 4. Kwee, B., Some theorems on Nörlund summabiiity, Proc. London Math. Soc. 14, (1964), 353–368. Google Scholar

[5] 5. Mears, F. M., Absolute regularity and the Nörlund mean, Ann. of Math. 38 (1937), 594–601. Google Scholar

[6] 6. Miesner, W., The convergence fields of Nörlund means, Proc. London Math. Soc. 15 (1965), 495–507. Google Scholar

[7] 7. Peyerimhoff, A., On convergence fields of Nörlund means, Proc. Amer. Math. Soc. 7 (1956), 335–347. Google Scholar

[8] 8. Zygmund, A., Trigometric series (Cambridge University Press, London, 1959). Google Scholar

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