Multisummability of formal power series solutions of linear analytic \(q\)-difference equations. (Multisommabilité des séries entières solutions formelles d’une équation aux \(q\)-différences linéaire analytique.) (French) Zbl 1063.39001

Summary: We introduce a \(q\)-analogous version of the elementary acceleration method of Écalle-Martinet-Ramis and define the \(Gq\)-multisummable power series. We show that every formal power series satisfying a linear analytic \(q\)-difference equation is \(Gq\)-multisummable.


39A10 Additive difference equations
40G99 Special methods of summability
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