On considère des équations aux différences finies où prend ses valeurs dans et est méromorphe en au voisinage de dans et holomorphe en au voisinage de 0 dans . On montre que sous certaines conditions sur la partie linéaire de , des solutions formelles dans sont multisommables. De plus on montre que ces solutions formelles se relèvent toujours en des solutions holomorphes dans des demi-plans supérieurs et inférieurs, mais généralement ces solutions ne sont pas déterminées uniquement par les solutions formelles.
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.
@article{AIF_1996__46_1_183_0, author = {Braaksma, Boele L. J. and Faber, Bernard F.}, title = {Multisummability for some classes of difference equations}, journal = {Annales de l'Institut Fourier}, pages = {183--217}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {46}, number = {1}, year = {1996}, doi = {10.5802/aif.1511}, mrnumber = {97e:39002}, zbl = {0837.39001}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1511/} }
TY - JOUR AU - Braaksma, Boele L. J. AU - Faber, Bernard F. TI - Multisummability for some classes of difference equations JO - Annales de l'Institut Fourier PY - 1996 SP - 183 EP - 217 VL - 46 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1511/ DO - 10.5802/aif.1511 LA - en ID - AIF_1996__46_1_183_0 ER -
%0 Journal Article %A Braaksma, Boele L. J. %A Faber, Bernard F. %T Multisummability for some classes of difference equations %J Annales de l'Institut Fourier %D 1996 %P 183-217 %V 46 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1511/ %R 10.5802/aif.1511 %G en %F AIF_1996__46_1_183_0
Braaksma, Boele L. J.; Faber, Bernard F. Multisummability for some classes of difference equations. Annales de l'Institut Fourier, Tome 46 (1996) no. 1, pp. 183-217. doi : 10.5802/aif.1511. http://www.numdam.org/articles/10.5802/aif.1511/
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