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A note on composition operators on spaces of real analytic functions

Paweł Domański, Michał Goliński, Michael Langenbruch (2012)

Annales Polonici Mathematici

We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semiproper map φ such that the associated composition operator is not open onto its image.

Analytic functions are -density continuous

Krzysztof Ciesielski, Lee Larson (1994)

Commentationes Mathematicae Universitatis Carolinae

A real function is -density continuous if it is continuous with the -density topology on both the domain and the range. If f is analytic, then f is -density continuous. There exists a function which is both C and convex which is not -density continuous.

Analytical properties of power series on Levi-Civita fields

Khodr Shamseddine, Martin Berz (2005)

Annales mathématiques Blaise Pascal

A detailed study of power series on the Levi-Civita fields is presented. After reviewing two types of convergence on those fields, including convergence criteria for power series, we study some analytical properties of power series. We show that within their domain of convergence, power series are infinitely often differentiable and re-expandable around any point within the radius of convergence from the origin. Then we study a large class of functions that are given locally by power series and...

Bernstein’s analyticity theorem for quantum differences

Tord Sjödin (2007)

Czechoslovak Mathematical Journal

We consider real valued functions f defined on a subinterval I of the positive real axis and prove that if all of f ’s quantum differences are nonnegative then f has a power series representation on I . Further, if the quantum differences have fixed sign on I then f is analytic on I .

Extending analyticK-subanalytic functions

Artur Piękosz (2004)

Open Mathematics

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.

Extending Tamm's theorem

Lou van den Dries, Chris Miller (1994)

Annales de l'institut Fourier

We extend a result of M. Tamm as follows:Let f : A , A m + n , be definable in the ordered field of real numbers augmented by all real analytic functions on compact boxes and all power functions x x r : ( 0 , ) , r . Then there exists N such that for all ( a , b ) A , if y f ( a , y ) is C N in a neighborhood of b , then y f ( a , y ) is real analytic in a neighborhood of b .

Fonctions de type trace

Daniel Barlet (1983)

Annales de l'institut Fourier

Soit π : V W un morphisme propre fini et surjectif entre deux variétés analytiques complexes. Nous donnons une caractérisation des fonctions (continues) sur W qui sont de la forme π * f f est une fonction C sur V . Pour cela nous introduisons la notion de fonction de type trace sur une variété analytique complexe. Ces fonctions sont analytiques réelles en dehors d’une hypersurface complexe et admettent des singularités très simples aux points de cette hypersurface.

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