Emmanuel Mazzilli

Zero varieties for the Nevanlinna class on all convex domains of finite type

Abstract. It is shown, that the so-called Blaschke condition characterizes in any bounded smooth convex domain of finite type exactly the divisors which are zero sets of functions of the Nevanlinna class on the domain. The main tool is a non-isotropic L estimate for solutions of the Cauchy-Riemann equations on such domains, which are obtained by estimating suitable kernels of BerndtssonAndersson type.

Bohr’s Phenomenon on a Regular Condenser in the Complex Plane

We prove the following generalization of Bohr’s Theorem: let

Estimates for the Bohr Radius of a Faber–Green Condenser in the Complex Plane

K\subset{\rm C}

Variétés singulières et extension des fonctions holomorphes

be a continuum,

Extension and restriction of holomorphic functions

(F_{K,n})_{n\geq 0}

Regular type of real hyper-surfaces in (almost) complex manifolds

its Faber polynomials, ωnr the level sets of the Green function of ℂ K with singularity at infinity. Then there exists a radius

Extension of bounded holomorphic functions¶in convex domains

R_{0}>0

Division des distributions et applications à l'étude d'idéaux de fonctions holomorphes

such that for any

The Bohr radius for an elliptic condenser

f=\sum_{n}a_{n}F_{K,n}\in {O}(\Omega_{R_0})

A remark on the theorem of Ohsawa-Takegoshi

with