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Extension of Whitney fields from subanalytic sets. (English) Zbl 0404.58010


MSC:

58C25 Differentiable maps on manifolds
32B20 Semi-analytic sets, subanalytic sets, and generalizations
58K99 Theory of singularities and catastrophe theory
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References:

[1] Bierstone, E., Milman, P.: Extension and lifting ofC ? Whitney fields. L’Enseignement Math.23, 129-137 (1977) · Zbl 0356.58004
[2] Glaeser, G.: Fonctions composées différentiables. Ann. of Math.77, 193-209 (1963) · Zbl 0106.31302 · doi:10.2307/1970204
[3] Hironaka, H.: Introduction to real-analytic sets and real-analytic maps. Istituto Matematico ?L. Tonelli?, Pisa, Italy (1973)
[4] Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero: I, II. Ann. of Math.79, 109-326 (1964) · Zbl 0122.38603 · doi:10.2307/1970486
[5] Hironaka, H.: Subanalytic sets. Number Theory, Algebraic Geometry and Commutative Algebra, in honor of Y. Akizuki, pp. 453-493. Tokyo: Kinokuniya 1973
[6] ?ojasiewicz, S.: Ensembles semi-analytiques. Inst. Hautes Études Sci., Bures-sur-Yvette, France (1964) · Zbl 0128.17101
[7] ?ojasiewicz, S.: Sur le problème de la division. Studia Math.8, 87-136 (1959) · Zbl 0115.10203
[8] ?ojasiewicz, S.: Whitney fields and the Malgrange-Mather preparation theorem, Proceedings of Liverpool Singularities Symposium I. Lecture Notes in Math. No. 192, pp. 106-115. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0224.58003
[9] Milman, P.: On the nonexistence of a projection from functions ofx to functions ofx n . Proc, Amer. Math. Soc.63, 87-90 (1977) · Zbl 0351.26024
[10] Mityagin, B.: Approximate dimension and bases in nuclear spaces. Russian Math. Surveys16, 59-128 (1961) · Zbl 0104.08601 · doi:10.1070/RM1961v016n04ABEH004109
[11] Seeley, R.T.: Extension ofC ? functions defined in a half space. Proc. Amer. Math. Soc.15, 625-626 (1964) · Zbl 0127.28403
[12] Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton: University Press 1970 · Zbl 0207.13501
[13] Tougeron, J.-Cl.: Idéaux de Fonctions Différentiables. Berlin, Heidelberg, New York: Springer 1972
[14] Whitney, H.: Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc.36, 63-89 (1934) · Zbl 0008.24902 · doi:10.1090/S0002-9947-1934-1501735-3
[15] Zariski, O.: Exceptional singularities of an algebroid surface and their reduction. Rend. Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Natur43, 135-146 (1967) · Zbl 0168.18903
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