Bo Berndtsson

Bergman kernels and the pseudoeffectivity of relative canonical bundles

A criterion for the pseudoeffectivity of (twisted ) relative canonical bundles of surjective projective maps.

Interpolating sequences for H∞ in the ball

Abstract We give a sufficient condition for a sequence of points in the unit ball of ℂ n to be an interpolating sequence for H ∞ . This result generalizes Carlesons interpolation theorem in one complex variable, but an example shows that the condition is not necessary when n ≥1.

A note on Pavlov-Korevaar-Dixon interpolation

Abstract In [3] Korevaar and Dixon have considered an interpolation problem for entire functions (stemming from work by Pavlov [4]), which is connected with Muntz — approximation on arcs and Macintyres conjecture. In this note we give a characterization of interpolation sequences in terms of a “uniform separation condition”. We also give an explicit example which shows that a condition for interpolation sequences in [3] is essentially best possible of its kind.

Integral Formulas and the Ohsawa- Takegoshi Extension Theorem

AbstractWe construct a semiexplicit integral representation of the canonical solution to the

Uniform estimates with weights for the\(\bar \partial - equation\)

\bar \partial

Lelong Numbers and Vector Bundles

-equation with respect to a plurisubharmonic weight function in a pseudoconvex domain. The construction is based on a construction related to the Ohsawa-Takegoshi extension theorem combined with a method to construct weighted integral representations due to M. Andersson.

Almost holomorphic extensions of ultradifferentiable functions

The aim of this note is to give some estimates for the number of zeros of analytic functions of several variables. In particular we will study functions bounded in tube domains and entire functions of finite order. Special attention will be directed to real zeros or zeros that lie close to the reals. A general reference for the corresponding questions in one variable is Boas [1]. In one variable a basic and trivial fact is that the number of real zeros does not exceed the total number of zeros. In section 2 we give a corresponding statement for p-dimensional analytic varieties in C n, i.e. we compare the p-dimensional measure of the variety intersected with R n with the 2p-dimensional measure of the whole variety. This comparison results from the following theorem which is inspired by a result by Lelong [4].

A Comparison Principle for Bergman Kernels

AbstractThis paper concernsL∞-variants of Hörmanders weightedL2-estimates for the