Related papers: Holomorphic extension of the de Gennes function

The main purpose of this article is to present a generalization of Forelli's theorem for the functions holomorphic along a general pencil of holomorphic discs. This generalizes the main result of \cite{JKS13} and the original Forelli's…

We prove some extension theorems for quaternionic holomorphic functions in the sense of Fueter. Starting from the existence theorem for the nonhomogeneous Cauchy-Riemann-Fueter Problem, we prove that an $\mathbb{H}$-valued function $f$ on a…

Let D be a strictly convex domain and X be a singular analytic subset of C^2 such that the intersection of X and D is non empty. We give conditions under which a function holomophic on the intersection of X and D can be extended…

The aim of this note is to provide a new identity connected with the Gauss hypergeometric function. This is achieved using results of certain combinatorial identities and a hypergeometric function approach.

The reflection function of a smooth CR diffeomorphism between two minimal real analytic hypersurfaces is everywhere real analytic.

I present a simple derivation of the de Gennes narrowing phenomenon.

An extension theorem for holomorphic mappings between two domains in $\mathbb C^2$ is proved under purely local hypotheses.

Let $D\subset \C^n,$ $G\subset \C^m$ be pseudoconvex domains, let $A$ (resp. $B$) be an open subset of the boundary $\partial D$ (resp. $\partial G$) and let $X$ be the 2-fold cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$ Suppose in…

In this paper we examinate some phenomena arising when a holomorphic germ is analytically continued.

We gave an alternative short proof on the finite generation of holomorphic functions with polynomial growth on Riemann surfaces with nonnegative curvature. The first proof was due to Li and Tam.

Let $\mathbb{B}^2$ denote the open unit ball in $\mathbb{C}^2$, and let $p\in \mathbb{C}^2\setminus\overline{\mathbb{B}^2}$. We prove that if $f$ is an analytic function on the sphere $\partial\mathbb{B}^2$ that extends holomorphically in…

We establish analytic linearization of s-proper analytic groupoids around invariant submanifolds. We apply this result to show that any such groupoid admits a holomorphic extension.

The aim of this note is to establish an interesting hypergeometric generating relation contiguous to that of Exton by a short method.

We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles

The paper gives the following characterization of the disc algebra in terms of the argument principle: A continuous function f on the unit circle T extends holomorphically through the unit disc if and only if for each polynomial P such that…

The purpose of the present note is two-fold. First, to show that deformations of algebras of smooth functions can be used to construct topologically nontrivial standard central extensions of loop groups. Second, to use noncommutative…

We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and…

We consider a formal power series in one variable whose coefficients are holomorphic functions in a given multidimensional complex domain. Assume the following two conditions on the series. (C1) The restriction of the series at each point…

It is known that a real analytic CR function f on a real analytic, generic submanifold M in C^N can be holomorphically extended. A stronger result on a finite type, real analytic, generic submanifold M is found in which we assume f a…

Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…