Multisummability for some classes of difference equations

Boele L. J. Braaksma; Bernard F. Faber

Displaying similar documents to “Multisummability for some classes of difference equations”

Variations of complex structures on an open Riemann surface

M. S. Narasimhan (1961)

Annales de l'institut Fourier

Similarity:

Soit $U_{1}$ un ouvert dans $C^{m}$ . Soit $π_{1} : S \to U_{1}$ une famille holomorphe de structures complexes sur une surface de Riemann non-compacte $M$ , avec $S_{t_{0}} = π_{1}^{- 1} (t_{0}) = M$ . ( $S = S (M \times U_{1})$ est une structure complexe sur le produit différentiable $M \times U_{1}$ ). Soit $M_{1}$ un domaine relativement compact dans $M$ . On démontre : pour tout voisinage de Stein $U$ de $t_{0}$ , assez petit, la famille $π_{1} : S (M_{1} \times U) \to U$ est isomorphe à la famille $π : Ω \to π (Ω)$ , où $Ω$ est un de la variété produit $M \times C^{m}$ , $π$ étant la projection $M \times C^{m} \to C^{m}$ . On donne aussi un résultat analogue pour le cas des variations différentiables. ...

Holomorphic series expansion of functions of Carleman type

Taib Belghiti (2004)

Annales Polonici Mathematici

Similarity:

Let f be a holomorphic function of Carleman type in a bounded convex domain D of the plane. We show that f can be expanded in a series f = ∑ₙfₙ, where fₙ is a holomorphic function in Dₙ satisfying $s u p_{z \in D ₙ} | f ₙ (z) | \leq C ϱ ⁿ$ for some constants C > 0 and 0 < ϱ < 1, and where (Dₙ)ₙ is a suitably chosen sequence of decreasing neighborhoods of the closure of D. Conversely, if f admits such an expansion then f is of Carleman type. The decrease of the sequence Dₙ characterizes the smoothness of f. ...

A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces

Viêt-Anh Nguyên (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Using recent development in Poletsky theory of discs, we prove the following result: Let $X,$ $Y$ be two complex manifolds, let $Z$ be a complex analytic space which possesses the Hartogs extension property, let $A$ (resp. $B$ ) be a non locally pluripolar subset of $X$ (resp. $Y$ ). We show that every separately holomorphic mapping $f : W : = (A \times Y) \cup (X \times B) \to Z$ extends to a holomorphic mapping $\hat{f}$ on $\hat{W} : = \{(z, w) \in X \times Y : \tilde{ω} (z, A, X) + \tilde{ω} (w, B, Y) < 1\}$ such that $\hat{f} = f$ on $W \cap \hat{W},$ where $\tilde{ω} (\cdot, A, X)$ (resp. $\tilde{ω} (\cdot, B, Y))$ is the plurisubharmonic measure of $A$ (resp. $B$ ) relative to $X$ (resp. $Y$ ). Generalizations...

On functional linear partial differential equations in Gevrey spaces of holomorphic functions.

Stéphane Malek (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

We investigate existence and unicity of global sectorial holomorphic solutions of functional linear partial differential equations in some Gevrey spaces. A version of the Cauchy-Kowalevskaya theorem for some linear partial $q$ -difference-differential equations is also presented.

Henkin-Ramirez formulas with weight factors

B. Berndtsson, Mats Andersson (1982)

Annales de l'institut Fourier

Similarity:

We construct a generalization of the Henkin-Ramírez (or Cauchy-Leray) kernels for the $\overline{\partial}$ -equation. The generalization consists in multiplication by a weight factor and addition of suitable lower order terms, and is found via a representation as an “oscillating integral”. As special cases we consider weights which behave like a power of the distance to the boundary, like exp- $ϕ$ with $ϕ$ convex, and weights of polynomial decrease in $C^{n}$ . We also briefly consider kernels with singularities on...

Determination of the pluripolar hull of graphs of certain holomorphic functions

Armen Edigarian, Jan Wiegerinck (2004)

Annales de l’institut Fourier

Similarity:

Let $A$ be a closed polar subset of a domain $D$ in $ℂ$ . We give a complete description of the pluripolar hull $Γ_{D \times ℂ}^{*}$ of the graph $Γ$ of a holomorphic function defined on $D ∖ A$ . To achieve this, we prove for pluriharmonic measure certain semi-continuity properties and a localization principle.