Extending analyticK-subanalytic functions

Artur Piękosz

Open Mathematics (2004)

  • Volume: 2, Issue: 3, page 362-367
  • ISSN: 2391-5455

Abstract

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Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝanK, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū.

How to cite

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Artur Piękosz. "Extending analyticK-subanalytic functions." Open Mathematics 2.3 (2004): 362-367. <http://eudml.org/doc/268854>.

@article{ArturPiękosz2004,
abstract = {Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝanK, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū.},
author = {Artur Piękosz},
journal = {Open Mathematics},
keywords = {Primary: 14P15, 26E05, 32B20; Second: 30B40, 03C64},
language = {eng},
number = {3},
pages = {362-367},
title = {Extending analyticK-subanalytic functions},
url = {http://eudml.org/doc/268854},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Artur Piękosz
TI - Extending analyticK-subanalytic functions
JO - Open Mathematics
PY - 2004
VL - 2
IS - 3
SP - 362
EP - 367
AB - Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝanK, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū.
LA - eng
KW - Primary: 14P15, 26E05, 32B20; Second: 30B40, 03C64
UR - http://eudml.org/doc/268854
ER -

References

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  1. [1] E. Bierstone: “Control of radii of convergence and extension of subanalytic functions,Proc. of the Amer. Math. Soc., Vol. 132, (2004), pp. 997–1003. http://dx.doi.org/10.1090/S0002-9939-03-07191-0 Zbl1082.32002
  2. [2] E. Bierstone, P. Milman: “Semianalytic and subanalytic sets”,Inst. Hautes Études Sci. Publ. Math., Vol. 67, (1988), pp 5–42. Zbl0674.32002
  3. [3] L. van den Dries: “A generalization of the Tarski-Seidenberg theorem and some nondefinability results”,Bull. Amer. Math. Soc. (N. S.) Vol. 15, (1986), pp. 189–193. http://dx.doi.org/10.1090/S0273-0979-1986-15468-6 Zbl0612.03008
  4. [4] L. van den Dries, C. Miller: “Extending Tamm's theorem”,Ann. Inst. Fourier, Grenoble, Vol. 44, (1994), pp. 1367–1395. Zbl0816.32004
  5. [5] L. van den Dries, C. Miller: “Geometric categories and o-minimal structures”,Duke Math. Journal, Vol. 84, (1996), pp. 497–540. http://dx.doi.org/10.1215/S0012-7094-96-08416-1 Zbl0889.03025
  6. [6] J.-M. Lion, J.-Ph. Rolin: “Théorème de préparation pour les fonctions logarithmico-exponentielles”,Ann. Inst. Fourier, Grenoble, Vol. 47, (1997), 859–884. Zbl0873.32004
  7. [7] C. Miller: “Expansion of the real field with power functions”,Ann. Pure Appl. Logic, Vol. 68, (1994), pp. 79–84 http://dx.doi.org/10.1016/0168-0072(94)90048-5 
  8. [8] A. Piękosz: “K-subanalytic rectilinearization and uniformization”,Central European Journal of Mathematics, Vol. 1, (2003), pp. 441–456. http://dx.doi.org/10.2478/BF02475178 Zbl1038.32010
  9. [9] J.-Cl. Tougeron: “Paramétrisations de petit chemins en géométrie analytique réele”,Singularities and differential equations (Warsaw 1993), Banach Center Publications, Vol. 33, (1996), pp. 421–436. 

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