Håkan Samuelsson Kalm

VARIOUS APPROACHES TO PRODUCTS OF RESIDUE CURRENTS

We describe various approaches to Coleff-Herrera products of residue currents R (of Cauchy-Fantappiè-Leray type) associated to holomorphic mappings fj. More precisely, we study to which extent (exterior) products of natural regularizations of the individual currents R yield regularizations of the corresponding Coleff-Herrera products. Our results hold globally on an arbitrary pure-dimensional complex space.

Presence or absence of analytic structure in maximal ideal spaces

We study extensions of Wermer’s maximality theorem to several complex variables. We exhibit various smoothly embedded manifolds in complex Euclidean space whose hulls are non-trivial but contain no analytic disks. We answer a question posed by Lee Stout concerning the existence of analytic structure for a uniform algebra whose maximal ideal space is a manifold.

One parameter regularizations of products of residue currents

We show that Coleff–Herrera type products of residue currents can be defined by analytic continuation of natural functions depending on one complex variable.