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Displaying similar documents to “Smooth and analytic solutions for analytic linear systems.”

Relations among analytic functions. I

Edward Bierstone, P. D. Milman (1987)

Annales de l'institut Fourier

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Neither real analytic sets nor the images of real or complex analytic mappings are, in general, coherent. Let Φ : X → Y be a morphism of real analytic spaces, and let Ψ : 𝒢 → ℱ be a homomorphism of coherent modules over the induced ring homomorphism Φ * : 𝒪 Y → 𝒪 X . We conjecture that, despite the failure of coherence, certain natural discrete invariants of the modules of formal relations ℛ a = Ker Ψ ^ a , a ∈ X , are upper semi-continuous in the analytic Zariski topology of X . We prove semicontinuity in many cases (e.g. in the algebraic...

On the analytic approximation of differentiable functions from above

Alessandro Tancredi, Alberto Tognoli (2002)

Bollettino dell'Unione Matematica Italiana

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We determine conditions in order that a differentiable function be approximable from above by analytic functions, being left invariate on a fixed analytic subset which is a locally complete intersection.

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.