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Subanalytic blow-  functions
Author(s):
Andreas
Fischer;
Krzysztof
Kurdyka
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2285-2291.
MSC (2000):
Primary 32B20, 14P10;
Secondary 03C64, 14E15, 14P15, 32C05, 58A07
Posted:
February 12, 2009
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Abstract:
We describe rings of subanalytic functions which become continuously differentiable after finitely many local blowings-up with analytic centers.
References:
-
- 1.
- E. Bierstone and P. D. Milman, Semianalytic and subanalytic sets. Inst. Hautes Études Sci. Publ. Math. 67 (1988), 5-42. MR 972342 (89k:32011)
- 2.
- E. Bierstone and P. D. Milman, Arc-analytic functions. Invent. Math. 101 (1990), 411-424. MR 1062969 (92a:32011)
- 3.
- E. Bierstone, P. Milman and A. Parusiński, A function which is arc-analytic but not continuous. Proc. Amer. Math. Soc. 113 (1991), no. 2, 419-423. MR 1072083 (91m:32008)
- 4.
- J. Boman, Differentiability of a function and of its compositions with functions of one variable. Math. Scand. 20 (1967), 249-268. MR 0237728 (38:6009)
- 5.
- M. Coste, T. Fukui, K. Kurdyka, C. McCrory, A. Parusiński and L. Paunescu, Arc spaces and additive invariants in Real Algebraic and Analytic Geometry. Panoramas et Synthèses 24, Soc. Math. France (2007).
- 6.
- L. van den Dries and C. Miller, Geometric categories and o-minimal structures. Duke Math. J. 84 (1996), no. 2, 497-540. MR 1404337 (97i:32008)
- 7.
- A. Fischer, Peano-Differentiable Functions in O-Minimal Structures. Doctoral thesis, Universität Passau, 2006.
- 8.
- A. Fischer, Differentiability of Peano derivatives. Proc. Amer. Math. Soc. 136 (2008), 1779-1785. MR 2373608
- 9.
- A. Fischer, Singularities of o-minimal Peano derivatives. Mathematische Nachrichten, accepted, 2008.
- 10.
- M. R. Hestenes, Extension of the range of a differentiable function. Duke Math. J. 8 (1941), 183-192. MR 0003434 (2:219c)
- 11.
- T.-C. Kuo, On classification of real singularities. Invent. Math. 82 (1985), 257-262. MR 809714 (87d:58025)
- 12.
- K. Kurdyka, Points réguliers d'un sous-analytique, Ann. Inst. Fourier (Grenoble) 38 (1988), 133-156. MR 0949002 (89g:32010)
- 13.
- K. Kurdyka, Ensembles semi-algébriques symétriques par arcs. Math. Ann. 282 (1988), 445-462. MR 967023 (89j:14015)
- 14.
- K. Kurdyka, An arc-analytic function with nondiscrete singular set. Ann. Polon. Math. 59, no. 3 (1994), 251-254. MR 1282776 (95g:32009)
- 15.
- K. Kurdyka and L. Paunescu, Arc-analyticity is an open property. Singularités Franco-Japonaises, 155-162, Sémin. Congr., 10, Soc. Math. France, Paris, 2005. MR 2145953 (2006c:32007)
- 16.
- S. Łojasiewicz, Ensembles semi-analytiques, preprint, Inst. Hautes Études Sci. (1965), accessible online: http://perso.univ-rennesl.fr/michel.coste/.
- 17.
- A. Parusiński, Subanalytic functions. Trans. Amer. Math. Soc. 344, no. 2 (1994), 583-595. MR 1160156 (94k:32006)
- 18.
- M. Shiota, Geometry of subanalytic and semialgebraic sets. Progress in Mathematics, 150. Birkhäuser Boston, Inc., Boston, MA, 1997. MR 1463945 (99b:14061)
- 19.
- M. Tamm, Subanalytic sets in the calculus of variation, Acta Math. 146 (1981), 167-199. MR 0611382 (82h:32012)
- 20.
- J. C. Tougeron, Idéaux des fonctions différentiables, Springer-Verlag, Berlin-New York, 1972. MR 0440598 (55:13472)
- 21.
- H. Whitney, Functions differentiable on the boundaries of regions, Ann. of Math. (2) 35 (1934), no. 3, 482-485. MR 1503174
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Additional Information:
Andreas
Fischer
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, S7N 5E6, Canada
Address at time of publication:
Fields Institute, 222 College Street, Toronto, Ontario, M5T 3J1, Canada
Email:
el.fischerandreas@web.de
Krzysztof
Kurdyka
Affiliation:
Laboratoire de Mathématiques LAMA, UMR-5127 CNRS, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France
Email:
kurdyka@univ-savoie.fr
DOI:
10.1090/S0002-9939-09-09643-9
PII:
S 0002-9939(09)09643-9
Keywords:
Subanalytic functions,
blowings-up,
arc-analytic function,
singularities
Received by editor(s):
March 13, 2008
Posted:
February 12, 2009
Additional Notes:
This research was partially supported by the NSERC discovery grant of Dr. Salma Kuhlmann
Communicated by:
Varghese Mathai
Copyright of article:
Copyright
2009,
American Mathematical Society
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