Geodesic
On Strong and Absolute Summability
Glasgow mathematical journal, Tome 4 (1960) no. 3, pp. 122-139

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

Suppose throughout that λ > 0, κ > - l. γ is real and thatThe series is said to be(i) summable (C, k) to s if (ii) strongly summable (C, k + 1) with index λ, or summable |C, k + 1|λ, to s if(iii) absolutely summable (C, k) with indices γ, λ, or summable |C, k + 1|λ, if 
Borwein, D. On Strong and Absolute Summability. Glasgow mathematical journal, Tome 4 (1960) no. 3, pp. 122-139. doi: 10.1017/S2040618500034043
@article{10_1017_S2040618500034043,
     author = {Borwein, D.},
     title = {On {Strong} and {Absolute} {Summability}},
     journal = {Glasgow mathematical journal},
     pages = {122--139},
     year = {1960},
     volume = {4},
     number = {3},
     doi = {10.1017/S2040618500034043},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034043/}
}
TY  - JOUR
AU  - Borwein, D.
TI  - On Strong and Absolute Summability
JO  - Glasgow mathematical journal
PY  - 1960
SP  - 122
EP  - 139
VL  - 4
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034043/
DO  - 10.1017/S2040618500034043
ID  - 10_1017_S2040618500034043
ER  - 
%0 Journal Article
%A Borwein, D.
%T On Strong and Absolute Summability
%J Glasgow mathematical journal
%D 1960
%P 122-139
%V 4
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034043/
%R 10.1017/S2040618500034043
%F 10_1017_S2040618500034043

[1] 1.Borwein, D., Theorems on some methods of summability, Quart. J. of Math. (2), 9 (1958), 310–316. Google Scholar | DOI

[2] 2.Chow, H. C., A further note on the summability of a power series on its circle of convergence, Ann. Acad. Sinica, 1 (1954), 559–567. Google Scholar

[3] 3.Flett, T. M., On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. London Math. Soc. (3), 7 (1957), 113–141. Google Scholar | DOI

[4] 4.Flett, T. M., Some more theorems concerning the absolute summability of Fourier series and power series, Proc. London Math. Soc. (3), 8 (1958), 357–387. Google Scholar | DOI

[5] 5.Flett, T. M., Some remarks on strong summability, Quart. J. of Math. 10 (1959), 115–139. Google Scholar | DOI

[6] 6.Glatfeld, M., On strong Rieszian summability, Proc. Glasgow Math. Assoc. 3 (1957), 123–131. Google Scholar | DOI

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

[8] 8.Hardy, G. H. and Littlewood, J. E., Some theorems concerning Dirichlet's series, Messenger of Math. 43 (1913–1914), 134–147. Google Scholar

[9] 9.Hardy, G. H., Littlewood, J. E. and Pólya, G., The maximum of a certain bilinear form, Proc. London Math. Soc. (2), 25 (1926), 265–282. Google Scholar | DOI

[10] 10.Hausdorff, F., Die Äquivalenz der Hölderschen und Cesàroschen Grenzwerte negativer Ordnung, Math. Z., 31 (1930), 186–196. Google Scholar | DOI

[11] 11.Hyslop, J. M., Note on the strong summability of series, Proc. Glasgow Math. Assoc. 1 (1951–1953), 16–20. Google Scholar | DOI

[12] 12.Knopp, K. and Lorentz, G. G., BeitrÄge zur absoluten Limitierung Archiv. der Math. 2 (1949), 10–16. Google Scholar | DOI

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

[14] 14.Morley, H., A theorem on Hausdorff transformations and its application to Cesàro and Hölder means, J. London Math. Soc. 25 (1950), 168–173. Google Scholar | DOI

[15] 15.Rogosinski, W. W., On Hausdorff methods of summability, Proc. Cambridge Phil. Soc. 38 (1942), 166–192. Google Scholar | DOI

[16] 16.Zygmund, A., Remarque sur la sommabilité des séries de fonctions orthogonales, Bull, de l'Acad. Pol. Serie A, (1926), 185–191. Google Scholar

Cité par Sources :