Sur la composition de séries formelles à croissance contrôlée
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 73-92.

Let F be a holomorphic map from s to s defined in a neighborhood of zero such that F(0)=0. If the jacobian determinant of F is not identically zero, P. M. Eakin and G. A. Harris proved the following result: any formal power series 𝒜 such that 𝒜F is analytic is itself analytic. If the jacobian determinant of F is identically zero, they proved that the previous conclusion is no more true. J. Chaumat and A.-M. Chollet extended this result in the case of formal power series satisfying growth conditions, of Gevrey type for instance. The author gets similar results when the map F is no more holomorphic. The loss of regularity on 𝒜 is optimal.

Classification : 13F25, 13J05, 32A05
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Mouze, Augustin. Sur la composition de séries formelles à croissance contrôlée. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 73-92. http://www.numdam.org/item/ASNSP_2002_5_1_1_73_0/

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