Multisummability for some classes of difference equations
Annales de l'Institut Fourier, Volume 46 (1996) no. 1, pp. 183-217.

This paper concerns difference equations y(x+1)=G(x,y) where G takes values in C n and G is meromorphic in x in a neighborhood of in C and holomorphic in a neighborhood of 0 in C n . It is shown that under certain conditions on the linear part of G, formal power series solutions in x -1/p ,pN, 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.

On considère des équations aux différences finies y(x+1)=G(x,y)G prend ses valeurs dans C n et G est méromorphe en x au voisinage de dans C et holomorphe en y au voisinage de 0 dans C n . On montre que sous certaines conditions sur la partie linéaire de G, des solutions formelles dans C n [[x -1/p ]],pN, 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.

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     title = {Multisummability for some classes of difference equations},
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Braaksma, Boele L. J.; Faber, Bernard F. Multisummability for some classes of difference equations. Annales de l'Institut Fourier, Volume 46 (1996) no. 1, pp. 183-217. doi : 10.5802/aif.1511. https://aif.centre-mersenne.org/articles/10.5802/aif.1511/

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