Sur la composition de séries formelles à croissance contrôlée

Mouze, Augustin

Mouze, Augustin

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 73-92.

Résumé

Let $F$ be a holomorphic map from $ℂ^{s}$ to $ℂ^{s}$ 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 $𝒜 \circ F$ 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.

MR | 1 citation dans Numdam

Classification : 13F25, 13J05, 32A05

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     title = {Sur la composition de s\'eries formelles \`a croissance contr\^ol\'ee},
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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. https://www.numdam.org/item/ASNSP_2002_5_1_1_73_0/

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