Récemment, Tripathy - Jour. Ind. Math. Soc., 32 (1960), 141-154 - a démontré certains résultats sur la sommabilité absolue de Hausdorff de séries associées à des séries de Fourier et des séries qui s’y rattachent, résultats qui généralisent ceux démontrés par Mohanty sur la sommabilité absolue de Cesaro.
En procédant de façon analogue, l’auteur a généralisé les résultats de Cheng - Duke Math. Jour., 15 (1948), 17-27 - en les démontrant pour la sommabilité absolue de Hausdorff.
Recently, Tripathy - Jour. Ind. Math. Soc., 32 (1960), 141-154 - has proved some results on absolute Hausdorff summability of some series associated with Fourier series and its allied series, which generalise the results proved by Mohanty on absolute Cesaro summability. Proceeding on the similar lines, the author has generalised the results of Cheng - Duke Math. Jour., 15 (1948), 17-27 - by proving them on absolute Hausdorff summability.
@article{AIF_1971__21_3_173_0,
author = {Gupta, B. L.},
title = {On the {Hausdorff} summability of series associated with a {Fourier} and its allied series},
journal = {Annales de l'Institut Fourier},
pages = {173--179},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {21},
number = {3},
year = {1971},
doi = {10.5802/aif.384},
mrnumber = {49 #3426},
zbl = {0222.42006},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.384/}
}
TY - JOUR AU - Gupta, B. L. TI - On the Hausdorff summability of series associated with a Fourier and its allied series JO - Annales de l'Institut Fourier PY - 1971 SP - 173 EP - 179 VL - 21 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.384/ DO - 10.5802/aif.384 LA - en ID - AIF_1971__21_3_173_0 ER -
%0 Journal Article %A Gupta, B. L. %T On the Hausdorff summability of series associated with a Fourier and its allied series %J Annales de l'Institut Fourier %D 1971 %P 173-179 %V 21 %N 3 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.384/ %R 10.5802/aif.384 %G en %F AIF_1971__21_3_173_0
Gupta, B. L. On the Hausdorff summability of series associated with a Fourier and its allied series. Annales de l'Institut Fourier, Tome 21 (1971) no. 3, pp. 173-179. doi : 10.5802/aif.384. http://www.numdam.org/articles/10.5802/aif.384/
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[3] , On the “second theorem of consistency” for riesz summability (II), Jour. Lond. Math. Soc. 27 (1952), 207-217. | MR | Zbl
[4] , On the absolute Hausdorff summability of some series associated with Fourier series and its allied series, Jour. Ind., Math. Soc. 32 (1960) 141-154. | MR | Zbl
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