Displaying similar documents to “A remark on Hartogs' double series”

Behavior of holomorphic functions in complex tangential directions in a domain of finite type in C.

Sandrine Grellier (1992)

Publicacions Matemàtiques

Similarity:

Let Ω be a domain in C. It is known that a holomorphic function on Ω behaves better in complex tangential directions. When Ω is of finite type, the best possible improvement is quantified at each point by the distance to the boundary in the complex tangential directions (see the papers on the geometry of finite type domains of Catlin, Nagel-Stein and Wainger for precise definition). We show that this improvement is characteristic: for a holomorphic function, a regularity in complex tangential...

Rigidity of holomorphic isometries

Edoardo Vesentini (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

A rigidity theorem for holomorphic families of holomorphic isometries acting on Cartan domains is proved.

Holomorphic extension maps for spaces of Whitney jets.

Jean Schmets, Manuel Valdivia (2001)

RACSAM

Similarity:

The key result (Theorem 1) provides the existence of a holomorphic approximation map for some space of C-functions on an open subset of R. This leads to results about the existence of a continuous linear extension map from the space of the Whitney jets on a closed subset F of R into a space of holomorphic functions on an open subset D of C such that D ∩ R = RF.

A KAM phenomenon for singular holomorphic vector fields

Laurent Stolovitch (2005)

Publications Mathématiques de l'IHÉS

Similarity:

Let X be a germ of holomorphic vector field at the origin of and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are...

Existence domains for holomorphic L functions.

Nicholas J. Daras (1994)

Publicacions Matemàtiques

Similarity:

If Ω is a domain of holomorphy in C, having a compact topological closure into another domain of holomorphy U ⊂ C such that (Ω,U) is a Runge pair, we construct a function F holomorphic in Ω which is singular at every boundary point of Ω and such that F is in L(Ω), for any p ∈ (0, +∞).