On subanalytic solutions of linear difference equations

par M. Moulay Barkatou (XLIM - DMI)

jeudi 2 oct. 2014, 10:30 → 11:30 Europe/Paris

XR203 (Bâtiment XLIM)

We consider linear difference equations with polynomial coefficients over C and their solutions in the form of sequences indexed by the integers (sequential solutions). We investigate the C linear space of subanalytic solutions, i.e., those sequential solutions that are the restrictions to Z of some analytic solutions of the original equation. It is shown that this space coincides with the space of the restrictions to Z of entire solutions and that the dimension of this space is equal to the order of the original equation. This talk is based in a joint work with S. Abramov, M. van Hoeij and M. Petkovsek (J. Symb. Comput. 46(11): 1205-1228 (2011)).