Fonctions multisommables

Summation of formal solutions of a class of linear difference equations

“…[MR91]), or in a more abstract way (cf. [MR92]). In [Bal94] Balser presented yet another definition.…”

A new proof of multisummability of formal solutions of non linear meromorphic differential equations

“…We will prove multisummability of formal power series solutions of differential equation (2.1) according to the Malgrange-Ramis definition of multisummability [7]. This definition is slightly different from those of [I], [2], [3], [8] : one replaces the notion of multisummability in one direction by the notion of multisummability on a family {Ji,..., In} of nested closed arcs of the unit circle S (or more generally of its universal covering 5').…”

“…This definition is slightly different from those of [I], [2], [3], [8] : one replaces the notion of multisummability in one direction by the notion of multisummability on a family {Ji,..., In} of nested closed arcs of the unit circle S (or more generally of its universal covering 5'). In this paragraph we will use the definitions and notations of [7]. We will build a sequence (<^i,..., <^p, (j>p+i) with a) (f)j G (r^^l/.A^'""^-1 )) 7 ' 1 by a descending recursion on j.…”

“…Afterwards in [11] the second author outlined another proof based on the cohomological definition of multisummability (cf. B. Malgrange and J.-P. Ramis [7] and W. Balser, B.L.J. Braaksma, J.-P. Ramis and Y. Sibuya [1]).…”

Multisummability of formal power series solutions of nonlinear meromorphic differential equations

“…We use the description of this procedure given by Martinet and Ramis [13]. Equivalent forms of multisummability have been given by Balser [I], [2], Jurkat [10], Malgrange and Ramis [12], [15].…”