Functional equations in real-analytic functions

G. Belitskii; V. Tkachenko

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The real-analytic solutions of the Abel functional equation

G. Belitskii, Yu. Lyubich (1999)

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For the Abel equation on a real-analytic manifold a dynamical criterion of solvability in real-analytic functions is proved.

Equivalence of differentiable mappings and analytic mappings

Masahiro Shiota (1981)

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Relations among analytic functions. II

Edward Bierstone, P. D. Milman (1987)

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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 $𝒞^{\infty}$ 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.

A characterization of analytic functions of n real variables

J. Siciak (1970)

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Semianalytic and subanalytic sets

Edward Bierstone, Pierre D. Milman (1988)

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An embedding theorem for real analytic spaces

F. Acquistapace, F. Broglia, A. Tognoli (1979)

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Analytic functions in general analysis

Angus E. Taylor (1937)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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 $Φ : X \to Y$ be a morphism of real analytic spaces, and let $Ψ : 𝒢 \to ℱ$ be a homomorphism of coherent modules over the induced ring homomorphism $Φ^{*} : 𝒪_{Y} \to 𝒪_{X}$ . We conjecture that, despite the failure of coherence, certain natural discrete invariants of the modules of formal relations $ℛ_{a} = Ker {\hat{Ψ}}_{a}$ , $a \in X$ , are upper semi-continuous in the analytic Zariski topology of $X$ . We prove semicontinuity in many cases (e.g. in the algebraic...