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.

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},
volume = {21},
number = {3},
year = {1971},
doi = {10.5802/aif.384},
zbl = {0222.42006},
mrnumber = {49 #3426},
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
DA  - 1971///
SP  - 173
EP  - 179
VL  - 21
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/aif.384/
UR  - https://zbmath.org/?q=an%3A0222.42006
UR  - https://www.ams.org/mathscinet-getitem?mr=49 #3426
UR  - https://doi.org/10.5802/aif.384
DO  - 10.5802/aif.384
LA  - en
ID  - AIF_1971__21_3_173_0
ER  - 
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/

[1] M.T. Cheng, Summability factors of Fourier series, Duke Math. Jour : 15 (1948), 17-27. | MR 9,580d | Zbl 0030.24901

[2] G.H. Hardy, Divergent series. Oxford 1949. | MR 11,25a | Zbl 0032.05801

[3] B. Kuttner, On the “second theorem of consistency” for riesz summability (II), Jour. Lond. Math. Soc. 27 (1952), 207-217. | MR 13,738a | Zbl 0046.06302

[4] N. Tripathy, 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 41 #725 | Zbl 0192.42401

Cité par Sources :