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Displaying similar documents to “On the division of functions of class C r by real analytic functions”

Topological invariants of analytic sets associated with Noetherian families

Aleksandra Nowel (2005)

Annales de l’institut Fourier

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Let Ω ⊂ ℝ n be a compact semianalytic set and let ℱ be a collection of real analytic functions defined in some neighbourhood of Ω . Let Y ω be the germ at ω of the set ⋂ f ∈ ℱ f - 1 ( 0 ) . Then there exist analytic functions v 1 , v 2 , ... , v s defined in a neighbourhood of Ω such that 1 2 χ ( lk ( ω , Y ω ) ) = ∑ i = 1 s sgn v i ( ω ) , for all ω ∈ Ω .

Relations among analytic functions. II

Edward Bierstone, P. D. Milman (1987)

Annales de l'institut Fourier

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This is a sequel to “Relations among analytic functions I”, , , fasc. 1, [pp. 187-239]. We reduce to semicontinuity of local invariants the problem of finding 𝒞 ∞ solutions to systems of equations involving division and composition by analytic functions. We prove semicontinuity in several general cases : in the algebraic category, for “regular” mappings, and for module homomorphisms over a finite mapping.