Semialgebraic Whitney partition of unity | Vidéo | Carmin.tv

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Semialgebraic Whitney partition of unity

By Anna Valette

Appears in 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.

Information about the video

Date of recording 27/01/2025
Date of publication 14/02/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20295003
Cite this video 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

Domain(s)

Algebraic Geometry

Bibliography

BOCHNAK, Jacek, COSTE, Michel, et ROY, Marie-Françoise. Real algebraic geometry. Springer Science & Business Media, 2013.
CALDERÓN, Alberto Pedro et ZYGMUND, Antoni. Local properties of solutions of elliptic partial differential equations. Studia Mathematica 1961, vol 20 . p. 285-339. - https://bibliotekanauki.pl/articles/1387925.pdf
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
FISCHER, Andreas. Smooth functions in o-minimal structures. Advances in Mathematics, 2008, vol. 218, no 2, p. 496-514. - https://doi.org/10.1016/j.aim.2008.01.002
KOCEL-CYNK, Beata, PAWŁUCKI, Wiesław, et VALETTE, Anna. Approximation of singular semialgebraic sets by smooth ones with respect to the Hausdorff metric. Bulletin des Sciences Mathématiques, 2023, vol. 185, p. 103270. - http://dx.doi.org/10.1016/j.bulsci.2023.103270
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
PAWŁUCKI, Wiesław. A linear extension operator for Whitney fields on closed o-minimal sets. In : Annales de l'institut Fourier. 2008. p. 383-404. - https://doi.org/10.5802/aif.2355
PAWŁUCKI, Wiesław. Lipschitz cell decomposition in o-minimal structures I. Illinois Journal of Mathematics, 2008, vol. 52, no 3, p. 1045-1063. - https://doi.org/10.1215/ijm/1254403731
PECKER, Daniel. On Efroymson's extension theorem for Nash functions. Journal of Pure and Applied Algebra, 1985, vol. 37, p. 193-203. - https://doi.org/10.1016/0022-4049(85)90097-0
SHIOTA, Masahiro. Approximation theorems for Nash mappings and Nash manifolds. Transactions of the American Mathematical Society, 1986, vol. 293, no 1, p. 319-337. - https://doi.org/10.2307/2000284
STEIN, Elias M. Singular integrals and differentiability properties of functions. Princeton university press, 1970.
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
TOUGERON, Jean Claude. Ideaux de fonctions différentiables.Springer. 1972 - https://doi.org/10.1007/978-3-662-59320-2

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