Geodesic
Schwartz Functions on Real Algebraic Varieties
Canadian journal of mathematics, Tome 70 (2018) no. 5, pp. 1008-1037

Voir la notice de l'article provenant de la source Cambridge University Press

We define Schwartz functions, tempered functions, and tempered distributions on (possibly singular) real algebraic varieties. We prove that all classical properties of these spaces, defined previously on affine spaces and on Nash manifolds, also hold in the case of affine real algebraic varieties, and give partial results for the non-affine case.
DOI : 10.4153/CJM-2017-042-6
Mots-clés : 14P99, 14P05, 22E45, 46A11, 46F05, real algebraic geometry, Schwartz function, tempered distribution 
Elazar, Boaz; Shaviv, Ary. Schwartz Functions on Real Algebraic Varieties. Canadian journal of mathematics, Tome 70 (2018) no. 5, pp. 1008-1037. doi: 10.4153/CJM-2017-042-6
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-042-6/}
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[AG] [AG] Aizenbud, A. and Gourevitch, D., Schwartz functions on Nash manifolds. Int. Math. Res. Not. IMRN (2008), no. 5, Art. ID rnm 155, 37. http://dx.doi.org/10.1093/imrn/rnm155 Google Scholar

[BCR] [BCR] Bochnak, J., Coste, M., and Roy, M.-E., Real algebraic geometry. Ergebnisse der Mathematik und ihrer Grenzgebiete, 36, Springer-Verlag, Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03718-8 Google Scholar

[BM1] [BM1] Bierstone, E. and Milman, P. D., Semi-analytic and subanalytic sets. Inst. Hautes Études Sci. Publ. Math. 67 (1988), 5–42. Google Scholar

[BM2] [BM2] Bierstone, E. and Milman, P. D., Geometric and differential properties of subanalytic sets. Ann. of Math. 147 (1998), 731–785. http://dx.doi.Org/10.2307/120964 Google Scholar

[BMP1] [BMP1] Bierstone, E., Milman, P. D., and Pawlucki, W., Composite differential functions. Duke Math. J. 83 (1996), 607–620. http://dx.doi.org/10.1215/S0012-7094-96-08318-0 Google Scholar

[BMP2] [BMP2] Bierstone, E., Milman, P. D., and Pawlucki, W., Higher-order tangents and Fefferman's paper on Whitney's extension problem. Ann. of Math. 164 (2006), 361–370. http://dx.doi.org/10.4007/annals.2006.164.361 Google Scholar

[CS] [CS] Constantine, G. M. and Savits, T. H., A multivariante Faa di Bruno formula with applications. Trans. Amer. Math. Soc. 384 (1996), 503–520. http://dx.doi.org/10.1090/S0002-9947-96-01501-2 Google Scholar

[dC] [dC] du Cloux, F., Sur les représentations differentiates des groupes de Lie alégbriques. Ann. Sci. École Norm. Sup. 24 (1991), 257–318. http://dx.doi.Org/10.24033/asens.1628 Google Scholar

[F] [F] Fefferman, C., Whitney's extension problem for S“1. Ann. of Math. 164 (2006), 313–359. http://dx.doi.org/10.4007/annals.2006.164.313 Google Scholar

[J] [J] Jech, T., Set theory. The third millennium éd., Springer-Verlag, Berlin, 2003. Google Scholar

[L] [L] Lojasiewicz, S., On semi-analytic and subanalytic geometry. Banach Center Publ. 34 (1995), 89–104. Google Scholar

[M] [M] Merrien, J., Faisceaux analytiques semi-cohérents. Ann. Inst. Fourier (Grenoble) 30 (1980), 165–219. http://dx.doi.Org/10.5802/aif.813 Google Scholar

[P] [P] Pawlucki, W., Examples of functions Ck-extendable for each k finite, but not Cx-extendable. Banach Center Publ., 44, Polish Acad. Sci. Inst. Math., Warsaw, 1998, pp. 183-187. Google Scholar

[S] [S] Shiota, M., Geometry of subanalytic and semialgebraic sets. Progress in Mathematics, 150, Birkhâuser Boston, Inc., Boston, MA, 1997. http://dx.doi.Org/10.1007/978-1-4612-2008-4 Google Scholar

[T] [T] Trêves, F., Topological vector spaces, distributions and kernels. Academic Press, New York-London, 1967. Google Scholar

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