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Apparaît dans la collection : Logarithmic and non-archimedean methods in Singularity Theory - Thematic Month Week 1 / Méthodes logarithmiques et non-archimédiennes en théorie des singularités - Mois thématique semaine 1

This talk is based on a common work with Wieslaw Pawlucki and Beata Kocel-Cynk. I will present a notion of $\mathrm{\wedge }_{p}$-regular partition of unity which can be seen as a semialgebraic counterpart of Whitney partition of unity. This enables us to obtain a semialgebraic (or more generally definable) version of Calder´on Zygmund theorem on regularization of the distance function. Some more consequences will also be given.

Informations sur la vidéo

Données de citation

  • DOI 10.24350/CIRM.V.20295003
  • Citer cette vidéo Valette, Anna (27/01/2025). Semialgebraic Whitney partition of unity. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20295003
  • URL https://dx.doi.org/10.24350/CIRM.V.20295003

Bibliographie

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  • VAN DEN DRIES, Lou et MILLER, Chris. Geometric categories and o-minimal structures.Duke Math. J. Vol.84 n°, 1996. 497–540 - https://doi.org/10.1215/S0012-7094-96-08416-1
  • EFROYMSON, Gustave A. The extension theorem for Nash functions. In: Colliot-Thélène, JL., Coste, M., Mahé, L., Roy, MF. (eds) Géométrie Algébrique Réelle et Formes Quadratiques. Lecture Notes in Mathematics, vol 959. Springer, Berlin, Heidelberg 1982 . p. 343-357. - https://doi.org/10.1007/BFb0062262
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  • KURDYKA, Krzysztof et PAWŁUCKI, Wiesław. Subanalytic version of Whitney's extension theorem. Studia Math, 1997, vol. 124, no 3, p. 269-280. - http://dx.doi.org/10.4064/sm-124-3-269-280
  • KURDYKA, Krzysztof et PAWŁUCKI, Wiesław. O-minimal version of Whitney's extension theorem. Studia Mathematica, 2014, vol. 1, no 224, p. 81-96. - https://dx.doi.org/10.4064/sm224-1-4
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  • VALETTE, Anna et VALETTE, Guillaume. Approximations in globally subanalytic and Denjoy-Carleman classes. Advances in Mathematics, 2021, vol. 385, p. 107764. - http://dx.doi.org/10.1016/j.aim.2021.107764
  • SHIOTA, Masahiro et SHIOTA, Masahiro. Geometry of subanalytic and semialgebraic sets. Boston : Birkhäuser, 1997. - https://doi.org/10.1007/978-1-4612-2008-4
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