Ragnar Sigurdsson

Complex convexity and analytic functionals

1 Convexity in Real Projective Space.- 1.1 Convexity in real affine space.- 1.2 Real projective space.- 1.3 Convexity in real projective space.- 2 Complex Convexity.- 2.1 Linearly convex sets.- 2.2 ?-convexity: Definition and examples.- 2.3 ?-convexity: Duality and invariance.- 2.4 Open ?-convex sets.- 2.5 Boundary properties of ?-convex sets.- 2.6 Spirally connected sets.- 3 Analytic Functionals and the Fantappie Transformation.- 3.1 The basic pairing in affine space.- 3.2 The basic pairing in projective space.- 3.3 Analytic functionals in affine space.- 3.4 Analytic functionals in projective space.- 3.5 The Fantappie transformation.- 3.6 Decomposition into partial fractions.- 3.7 Complex Kergin interpolation.- 4 Analytic Solutions to Partial Differential Equations.- 4.1 Solvability in ?-convex sets.- 4.2 Solvability and P-convexity for carriers.- References.

A note on the classification of holomorphic harmonic morphisms

In this note we give a complete classification of those holomorphic maps φ:U→ℂn defined on open and connected subsets of ℂm which are harmonic morphisms.

LIMITS OF MULTIPOLE PLURICOMPLEX GREEN FUNCTIONS

Let Ω be a bounded hyperconvex domain in ℂn, 0 ∈ Ω, and Se a family of N poles in Ω, all tending to 0 as e tends to 0. To each Se we associate its vanishing ideal and pluricomplex Green function . Suppose that, as e tends to 0, converges to (local uniform convergence), and that (Ge)e converges to G, locally uniformly away from 0; then . If the Hilbert–Samuel multiplicity of is strictly larger than its length (codimension, equal to N here), then (Ge)e cannot converge to . Conversely, if is a complete intersection ideal, then (Ge)e converges to . We work out the case of three poles.

Relative extremal functions and characterization of pluripolar sets in complex manifolds

We study a disc formula for the relative extremal function for a subset of a complex manifold and apply it to give a description of pluripolar sets and polynomial hulls.

Mikael passare: Curriculum vitae

1959-01-01. Kjell Alrik Mikael Pettersson is born in Vasteras, Sweden. Mother: Britt Gunvor Emilia Pettersson, later with the family name Elfstrom. Father: Werner Siems. Stepfathers: Kjell Pettersson and Hans Elfstrom.

A note on weighted homogeneous Siciak–Zaharyuta extremal functions

We prove that for any given upper semicontinuous function

Convexity in Real Projective Space

\varphi

GREEN FUNCTIONS WITH SINGULARITIES ALONG COMPLEX SPACES

on an open subset

Plurisubharmonicity of envelopes of disc functionals on manifolds

E

Convolution equations in domains ofCn

of