On strong Rieszian summability
Glasgow mathematical journal, Tome 2 (1957) no. 3, pp. 123-131

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

Recently H.-E. Richert [10] introduced a new method of summability, for which he completely solved the “summability problem” for Dirichlet series, and which led also to an extension of our knowledge of the relations between the abscissae of ordinary and absolute Rieszian summability. This non-linear method, which may best be characterized by the notion “strong Rieszian summability” †, depends on three parameters, on the order k;, the type λ, and the index p;. While Richert's paper deals almost exclusively with the application of that method of summability in a specialized form (namely the case p = 2, λn=log n) to Dirichlet series, it is the object of the present paper, to consider the general theory of strong Rieszian summability.
Glatfeld, Martin. On strong Rieszian summability. Glasgow mathematical journal, Tome 2 (1957) no. 3, pp. 123-131. doi: 10.1017/S2040618500033578
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[1] 1.Boyd, A. V. & Hyslop, J. M., A definition for strong Rieszian summability and its relationship to strong Cesàro summability, Proc. Glasgow Math. Assoc., 1 (1952), 94–99. Google Scholar | DOI

[2] 2.Fekete, M., Vizsgálatok az absolut summabilis sorokrol, alkalmazassal a Dirichlot- és Fourier- sorokra, Math, és termész. ért, 32 (1914), 389–425. Google Scholar

[3] 3.Hardy, G. H., Divergent series (Oxford, 1949). Google Scholar

[4] 4.Hardy, G. H. & Littlewood, J. E., Some properties of fractional integrals, I, Math. Z., 27 (1928), 565–606. Google Scholar | DOI

[5] 5.Hardy, G. H. & Riesz, M., The general theory of Dirichle's series (Cambridge, 1915). Google Scholar

[6] 6.Hyslop, J. M., Note on the strong summability of series, Proc. Glasgow Math. Assoc. 1 (1952), 16–20. Google Scholar | DOI

[7] 7.Kogbetliantz, E., Sommation des séries et intégrales divergentes par les moyennes arithmétiques et typiques, Mémorial Sci. Math. Fascicule 51 (1931). Google Scholar

[8] 8.Kuttner, B., Note on strong summability, J. London Math. Soc, 21 (1946), 118–122. Google Scholar

[9] 9.Obreschkoff, N., Über die absolute Summierung der Dirichletschen Reihen, Math. Z., 30 (1929), 375–386. Google Scholar | DOI

[10] 10.Richert, H. -E., Beitrage zur Summierbarkeit Dirichletscher Reihen mit Anwendungen auf dio Zahlentheorie, Nachr. Akad. Wiss. Göttingen, 1956, 77–125. Google Scholar

[11] 11.Titchmarsh, E. C., The theory of the Riemann zeta-function (Oxford, 1951). Google Scholar

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