An embedding theorem for real analytic spaces
F. Acquistapace, F. Broglia, A. Tognoli (1979)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Displaying similar documents to “Complex extensions”
An embedding theorem for real analytic spaces
Semianalytic and subanalytic sets
Edward Bierstone, Pierre D. Milman (1988)
Publications Mathématiques de l'IHÉS
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Equivalence of differentiable mappings and analytic mappings
Masahiro Shiota (1981)
Publications Mathématiques de l'IHÉS
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Schoenflies problems
M. Morse (1962)
Fundamenta Mathematicae
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Extending analyticK-subanalytic functions
Artur Piękosz (2004)
Open Mathematics
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Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝanK, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū.
The real-analytic solutions of the Abel functional equation
G. Belitskii, Yu. Lyubich (1999)
Studia Mathematica
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For the Abel equation on a real-analytic manifold a dynamical criterion of solvability in real-analytic functions is proved.
Embeddability of real analytic Cauchy-Riemann manifolds
Aldo Andreotti, Gregory A. Fredricks (1979)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Approximation theorems and Nash conjecture
Alberto Tognoli (1974)
Mémoires de la Société Mathématique de France
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K-analytic versus ccm-analytic sets in nonstandard compact complex manifolds
Rahim Moosa, Sergei Starchenko (2008)
Fundamenta Mathematicae
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It is shown that in an elementary extension of a compact complex manifold M, the K-analytic sets (where K is the algebraic closure of the underlying real closed field) agree with the ccm-analytic sets if and only if M is essentially saturated. In particular, this is the case for compact Kähler manifolds.
The Lie group of real analytic diffeomorphisms is not real analytic
Rafael Dahmen, Alexander Schmeding (2015)
Studia Mathematica
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We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense...