Geodesic
A Remark on the Gibbs Phenomenon and Lebesgue Constants for a Summability Method of Melikov
Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 301-303

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

Let u = ∑uk be a given series and let Melikov [4] has defined the n-th σ- transform of u by where ε and θ are assumed to be non-negative. This is easily shown to be equivalent to The method is a generalization of a method used by Kaufman [l], and of another one used by Melikov [5]. It reduces to the (n-l)th (C;l) mean when θ = 0 and ε = 0, and to the n-th (C;l) mean when θ = 1 and ε = 0. 
Ustina, Fred. A Remark on the Gibbs Phenomenon and Lebesgue Constants for a Summability Method of Melikov. Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 301-303. doi: 10.4153/CMB-1968-039-5
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[1] 1. Kaufman, B. L., Proceedings, Chkalovsky Pedagogical Institute, 11 (1957) 243-248. Google Scholar

[2] 2. Fejér, L., Lebesgueschen Konstanten und divergente Fourierreihen. J. Reine Angew. Math., 138(1910)22-53. Google Scholar

[3] 3. Lorch, L., The principal term in the asymptotic expansion of the Lebesgue constants. Amer. Math. Monthly, 61 (1954) 245-249. Google Scholar

[4] 4. Melikov, H.H., A class of summation methods for divergent series. (Russian). Proceedings of the Annual Scientific Conference, Kabardino-Balkarsk State University, 24 (1965) 183-188. Google Scholar

[5] 5. Melikov, H.H., Proceedings, Siberian-Ossetic State University, Math, and Natural Science Series, 26 (1964). Google Scholar

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