A linear extension operator for Whitney fields on closed o-minimal sets
Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 383-404.

A continuous linear extension operator, different from Whitney’s, for 𝒞 p -Whitney fields (p finite) on a closed o-minimal subset of n is constructed. The construction is based on special geometrical properties of o-minimal sets earlier studied by K. Kurdyka with the author.

On construit un opérateur d’extension linéaire et continu pour les champs de Whitney de classe 𝒞 p (p fini) sur un sous-ensemble fermé o-minimal de n . La construction, différente de celle de Whitney, est basée sur des propriétés géométriques spéciales des ensembles o-minimaux, étudiées avant par K. Kurdyka et l’auteur.

DOI: 10.5802/aif.2355
Classification: 26B05, 14P10, 32B20, 03C64
Keywords: Whitney field, extension operator, o-minimal structure, subanalytic set.
Mot clés : Champ de Whitney, opérateur d’extension, structure o-minimale, ensemble sous-analytique.
Pawłucki, Wiesław 1

1 Uniwersytet Jagielloński, Instytut Matematyki ul. Reymonta 4 30-059 Kraków (Poland)
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Pawłucki, Wiesław. A linear extension operator for Whitney fields on closed o-minimal sets. Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 383-404. doi : 10.5802/aif.2355. http://archive.numdam.org/articles/10.5802/aif.2355/

[1] Coste, M. An Introduction to O-minimal Geometry, Istituti Editoriali e Poligrafici Internazionali, Pisa-Roma, 2000

[2] van den Dries, L. Tame Topology and O-minimal Structures, Cambridge University Press, 1998 | MR | Zbl

[3] van den Dries, L.; Miller, C. Geometric categories and o-minimal structures, Duke Math. J., Volume 84 (1996), pp. 497-540 | DOI | MR | Zbl

[4] Glaeser, G. Étude de quelques algèbres tayloriennes, J. Anal. Math., Volume 6 (1958), pp. 1-124 | DOI | MR | Zbl

[5] Kurdyka, K. On a subanalytic stratification satisfying a Whitney property with exponent 1, Proc. Conference Real Algebraic Geometry, Springer, Rennes (1991), pp. 316-322 (LNM 1524) | MR | Zbl

[6] Kurdyka, K.; Pawłucki, W. Subanalytic version of Whitney’s extension theorem, Studia Math., Volume 124 (3) (1997), pp. 269-280 | Zbl

[7] Lion, J.-M.; Rolin, J.-P. Intégration des fonctions sous-analytiques et volumes des sous-ensembles sous-analytiques, Ann. Inst. Fourier, Grenoble, Volume 68,3 (1998), pp. 755-767 | DOI | Numdam | MR | Zbl

[8] Malgrange, B. Ideals of Differentiable Functions, Oxford University Press, 1966 | MR | Zbl

[9] Parusiński, A. Lipschitz stratification of subanalytic sets, Ann. Scient. Ec. Norm. Sup., Volume 27 (1994), pp. 661-696 | Numdam | MR | Zbl

[10] Pawłucki, W. A decomposition of a set definable in an o-minimal structure into perfectly situated sets, Ann. Polon. Math., Volume LXXIX.2 (2002), pp. 171-184 | DOI | Zbl

[11] Stein, E. M. Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970 | MR | Zbl

[12] Tougeron, J. Cl Idéaux des Fonctions Différentiables, Springer, 1972 | MR | Zbl

[13] Whitney, H. Analytic extensions of differentiable functions defined in closed sets, Trans. Am. Math. Soc., Volume 36 (1934), pp. 63-89 | DOI | MR | Zbl

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