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 1994802 | 1 citation dans Numdam

Classification : 13F25, 13J05, 32A05

BibTeX
RIS

@article{ASNSP_2002_5_1_1_73_0,
     author = {Mouze, Augustin},
     title = {Sur la composition de s\'eries formelles \`a croissance contr\^ol\'ee},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {73--92},
     publisher = {Scuola normale superiore},
     volume = {5e s{\'e}rie, 1},
     number = {1},
     year = {2002},
     mrnumber = {1994802},
     language = {fr},
     url = {http://archive.numdam.org/item/ASNSP_2002_5_1_1_73_0/}
}

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JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2002
DA  - 2002///
SP  - 73
EP  - 92
VL  - 5e s{\'e}rie, 1
IS  - 1
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_2002_5_1_1_73_0/
UR  - https://www.ams.org/mathscinet-getitem?mr=1994802
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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://archive.numdam.org/item/ASNSP_2002_5_1_1_73_0/

Bibliographie
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