For general matrix summability methods, we find necessary and sufficient conditions for such methods to be stronger than multisummability. In a second part we show the existence of power series which are not multisummable but can be summed by a matrix method satisfying the conditions mentioned above
Pour les méthodes matricielles générales de sommabilité nous donnons des conditions nécessaires et suffisantes qui rendent les méthodes plus puissantes que la multisommabilité. Dans une deuxième partie nous montrons l’existence d’une série entière qui n’est pas multisommable mais sommable par une méthode matricielle satisfaisant aux conditions indiquées dans la première partie
@article{AIF_1996__46_5_1349_0, author = {Balser, Werner and Beck, Andreas}, title = {Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability}, journal = {Annales de l'Institut Fourier}, pages = {1349--1357}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {46}, number = {5}, year = {1996}, doi = {10.5802/aif.1552}, zbl = {0864.34003}, mrnumber = {98e:40004}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1552/} }
TY - JOUR AU - Balser, Werner AU - Beck, Andreas TI - Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability JO - Annales de l'Institut Fourier PY - 1996 SP - 1349 EP - 1357 VL - 46 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1552/ DO - 10.5802/aif.1552 LA - en ID - AIF_1996__46_5_1349_0 ER -
%0 Journal Article %A Balser, Werner %A Beck, Andreas %T Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability %J Annales de l'Institut Fourier %D 1996 %P 1349-1357 %V 46 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1552/ %R 10.5802/aif.1552 %G en %F AIF_1996__46_5_1349_0
Balser, Werner; Beck, Andreas. Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability. Annales de l'Institut Fourier, Volume 46 (1996) no. 5, pp. 1349-1357. doi : 10.5802/aif.1552. https://aif.centre-mersenne.org/articles/10.5802/aif.1552/
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