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Implicit function theorem for locally blow-analytic functions. (English) Zbl 0996.58008
The author continues the investigations started in a previous paper [Pitman Res. Notes Math. Ser. 381, 62-63 (1998; Zbl 0896.58012)] where he found criteria for blow-analytic homeomorphisms. The present paper generalizes to arbitrary modifications some of the previous results where he treats mostly the case of toric modifications. Here he enlarges the category introduced in [T. Fukui, T.-C. Kuo and L. Paunescu, Ann. Inst. Fourier 51, No. 4, 1071-1087 (2001; Zbl 0984.32005)] to local blow-analytic functions allowing in this way apparently a larger class of modifications. The calculus generates difficulties because it is closed neither under differentiation nor integration, and also there is no global chain rule.
The general problem in locally convex spaces is considered in S. Yamamuro [A theory of differentiation in locally convex spaces, Mem. Am. Math. Soc. 212 (1979; Zbl 0464.58007)].

58C15 Implicit function theorems; global Newton methods on manifolds
32B20 Semi-analytic sets, subanalytic sets, and generalizations
58C05 Real-valued functions on manifolds
58K99 Theory of singularities and catastrophe theory
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