no. 5
Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability
Annales de l'Institut Fourier, Tome 46 (1996) no. 5, pp. 1349-1357.

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

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

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     title = {Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability},
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Balser, Werner; Beck, Andreas. Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability. Annales de l'Institut Fourier, Tome 46 (1996) no. 5, pp. 1349-1357. doi : 10.5802/aif.1552. http://www.numdam.org/articles/10.5802/aif.1552/

[1] W. Balser, From Divergent Power Series to Analytic Functions, Lecture Notes in Mathematics 1582, Springer-Verlag, 1994. | MR | Zbl

[2] A. Beck, Matrix-Summationsverfahren und Multisummierbarkeit, Dissertation, Ulm, 1995. | Zbl

[3] G.H. Hardy, Note on a divergent series, Proc. Cambridge Phil. Soc., (1941), 1-8. | JFM | MR | Zbl

[4] G.H. Hardy, Divergent Series, Oxford, 1956.

[5] W.B. Jurkat, Summability of asymptotic power series, Asympt. Anal., 7 (1993), 239-250. | MR | Zbl

[6] B. Malgrange, Sommation des séries divergentes, Expo. Math., 13 (1995), 163-222. | MR | Zbl

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