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Displaying similar documents to “Formal relations between quasianalytic functions of some fixed class”

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...

Weierstrass division theorem in quasianalytic local rings

Abdelhafed Elkhadiri, Hassan Sfouli (2008)

Studia Mathematica

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The main result of this paper is the following: if the Weierstrass division theorem is valid in a quasianalytic differentiable system, then this system is contained in the system of analytic germs. This result has already been known for particular examples, such as the quasianalytic Denjoy-Carleman classes.

Local analytic rings

Jorge C. Zilber (1990)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Analytic rings

Eduardo Dubuc, Gabriel Taubin (1983)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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On Witt rings of function fields of real analytic surfaces and curves.

Piotr Jaworski (1997)

Revista Matemática de la Universidad Complutense de Madrid

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Let V be a paracompact connected real analytic manifold of dimension 1 or 2, i.e. a smooth curve or surface. We consider it as a subset of some complex analytic manifold VC of the same dimension. Moreover by a prime divisor of V we shall mean the irreducible germ along V of a codimension one subvariety of VC which is an invariant of the complex conjugation. This notion is independent of the choice of the complexification VC. In the one-dimensional case prime divisors are just points,...