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On the summability of formal power series solutions of \(q\)-difference equations. II. (Sur la sommabilité des séries entières solutions formelles d’une équation aux \(q\)-différences. II.) (French) Zbl 0915.39004

Summary: [For part I see C. Zhang, Sur la sommabilité des séries entières solutions formelles d’une équation aux \(q\)-différences, ibid., 349-352 (1998)].
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.

MSC:

39A10 Additive difference equations
12H10 Difference algebra
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