Families of functions dominated by distributions of $C$-classes of mappings

Ishikawa, Goo

doi:10.5802/aif.924

Families of functions dominated by distributions of

C

-classes of mappings

Ishikawa, Goo

Annales de l'Institut Fourier, Tome 33 (1983) no. 2, pp. 199-217.

Résumé
Abstract

Un sous-faisceau du faisceau $ℰ_{Ω}$ des germes de fonctions $C^{\infty}$ sur un ouvert $Ω$ de $R^{n}$ est appelé un faisceau de sous-anneaux $C^{\infty}$ s’il est fermé pour l’opération définie par la composition avec toute fonction $C^{\infty}$ . En comparant avec les investigations de faisceaux d’idéaux de $ℰ_{Ω}$ , on étudie la présentabilité finie de certains faisceaux de sous-anneaux $C^{\infty}$ . En particulier, on traite le faisceau défini par la distribution de $𝒞$ -classes de Mather d’une application $C^{\infty}$ .

A subsheaf of the sheaf $ℰ_{Ω}$ of germs $C^{\infty}$ functions over an open subset $Ω$ of $R^{n}$ is called a sheaf of sub $C^{\infty}$ function. Comparing with the investigations of sheaves of ideals of $ℰ_{Ω}$ , we study the finite presentability of certain sheaves of sub $C^{\infty}$ -rings. Especially we treat the sheaf defined by the distribution of Mather’s $𝒞$ -classes of a $C^{\infty}$ mapping.

MR Zbl

DOI : 10.5802/aif.924

@article{AIF_1983__33_2_199_0,
     author = {Ishikawa, Goo},
     title = {Families of functions dominated by distributions of $C$-classes of mappings},
     journal = {Annales de l'Institut Fourier},
     pages = {199--217},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {33},
     number = {2},
     year = {1983},
     doi = {10.5802/aif.924},
     mrnumber = {84g:58014},
     zbl = {0488.58004},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.924/}
}

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Ishikawa, Goo. Families of functions dominated by distributions of $C$-classes of mappings. Annales de l'Institut Fourier, Tome 33 (1983) no. 2, pp. 199-217. doi : 10.5802/aif.924. https://www.numdam.org/articles/10.5802/aif.924/

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