Download PDF - Subanalytic version of Whitney's extension theoremAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Subanalytic version of Whitney's extension theorem

Authors 1, 2, 2

Affiliations

  1. Laboratoire de Mathématiques, Université de Savoie, Campus Scientifique, 73 376 Le Bourget-du-Lac Cedex, France
  2. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Abstract

For any subanalytic Ck-Whitney field (k finite), we construct its subanalytic Ck-extension to ℝn. Our method also applies to other o-minimal structures; e.g., to semialgebraic Whitney fields.

Bibliography

  1. E. Bierstone and P. D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ. Math. 67 (1988), 5-42.
  2. E. Bierstone and G. W. Schwarz, Continuous linear division and extension of C∞ functions, Duke Math. J. 50 (1983), 233-271.
  3. J. Bochnak, M. Coste et M.-F. Roy, Géométrie algébrique réelle, Springer, 1987.
  4. Z. Denkowska, S. Łojasiewicz and J. Stasica, Certaines propriétés élémentaires des ensembles sous-analytiques, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), 529-536.
  5. Z. Denkowska, Sur le théorème du complémentaire pour les ensembles sous-analytiques, ibid., 537-539.
  6. A. M. Gabrielov, Projections of semianalytic sets, Funktsional. Anal. i Prilozhen. 2 (4) (1968), 18-30 (in Russian).
  7. M. Gromov, Entropy, homology and semialgebraic geometry [after Y. Yomdin], Séminaire Bourbaki, 38ème année, 1985-86, no. 663; Astérisque 145-146 (1987), 225-240.
  8. H. Hironaka, Subanalytic sets, in: Number Theory, Algebraic Geometry and Commutative Algebra in Honor of Y. Akizuki, Kinokuniya, Tokyo, 1973, 453-493.
  9. K. Kurdyka, Points réguliers d'un sous-analytique, Ann. Inst. Fourier (Grenoble) 38 (1) (1988), 133-156.
  10. K. Kurdyka, On a subanalytic stratification satisfying a Whitney property with exponent 1, in: Proc. Conference Real Algebraic Geometry - Rennes 1991, Lecture Notes in Math. 1524, Springer, 1992, 316-322.
  11. S. Łojasiewicz, Ensembles semi-analytiques, Inst. Hautes Études Sci., Bures-sur-Yvette, 1964.
  12. S. Łojasiewicz, Sur la géométrie semi- et sous-analytique, Ann. Inst. Fourier (Grenoble) 43 (1993), 1575-1595.
  13. B. Malgrange, Ideals of Differentiable Functions, Oxford University Press, 1966.
  14. A. Parusiński, Lipschitz properties of semi-analytic sets, Ann. Inst. Fourier (Grenoble) 38 (4) (1988), 189-213.
  15. A. Parusiński, Lipschitz stratification of subanalytic sets, Ann. Sci. Ecole Norm. Sup. 27 (1994), 661-696.
  16. J. C. Tougeron, Idéaux de Fonctions Différentiables, Springer, 1972.
  17. L. van den Dries and C. Miller, Geometric categories and o-minimal structures, Duke Math. J. 84 (1996), 497-540.
  18. H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89.
  19. H. Whitney, Functions differentiable on the boundaries of regions, Ann. of Math. 35 (1934), 482-485.
Studia Mathematica
1997/124/3
Export to PBN, Opens in new tab
Pages:
269-280
Main language of publication
English
Received
1996-03-11
Accepted
1996-11-18
Published
1997
Exact and natural sciences