Matrix summability and a generalized Gibbs phenomenon.
Matrix transformations from absolutely convergent series to convergent sequences as general weighted mean summability methods.
Matrix transformations of starshaped sequences.
Matrixtransformationen dualer Folgenräume.
Mémoire sur les séries divergentes
Mercerian Theorems Involving Cesàro Means of Positive Order.
Multisommabilité des séries entières solutions formelles d’une équation aux -différences linéaire analytique
Nous introduisons une version -analogue du procédé d’accélération élémentaire d’Écalle-Martinet-Ramis et définissons la notion de série entière -multisommable. Nous montrons que toute série entière solution formelle d’une équation aux -différences linéaire analytique est -multisommable.
Multisummability for some classes of difference equations
This paper concerns difference equations where takes values in and is meromorphic in in a neighborhood of in and holomorphic in a neighborhood of 0 in . It is shown that under certain conditions on the linear part of , formal power series solutions in are multisummable. Moreover, it is shown that formal solutions may always be lifted to holomorphic solutions in upper and lower halfplanes, but in general these solutions are not uniquely determined by the formal solutions.
Multisummability of formal power series solutions of nonlinear meromorphic differential equations
In this paper a proof is given of a theorem of J. Écalle that formal power series solutions of nonlinear meromorphic differential equations are multisummable.