Extending analyticK-subanalytic functions

• Autorzy: Artur Piękosz
• Języki publikacji: EN

Abstrakty

EN

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\∑.

Słowa kluczowe

EN

Analytic extension; K-subanalytic; o-minimal; Primary: 14P15, 26E05, 32B20; Second: 30B40, 03C64

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 3
• Strony: 362-367

Daty

wydano

2004-06-01

online

2004-06-01

Twórcy

autor

Artur Piękosz

• Cracow University of Technology

Bibliografia

• [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
• [2] E. Bierstone, P. Milman: “Semianalytic and subanalytic sets”,Inst. Hautes Études Sci. Publ. Math., Vol. 67, (1988), pp 5–42.
• [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
• [4] L. van den Dries, C. Miller: “Extending Tamm's theorem”,Ann. Inst. Fourier, Grenoble, Vol. 44, (1994), pp. 1367–1395.
• [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
• [6] J.-M. Lion, J.-Ph. Rolin: “Théorème de préparation pour les fonctions logarithmico-exponentielles”,Ann. Inst. Fourier, Grenoble, Vol. 47, (1997), 859–884.
• [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] 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
• [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.

Identyfikatory

DOI

10.2478/BF02475232