Cauchy-Stieltjes integrals on strongly pseudoconvex domains
Removable sets for holomorphic functions of several complex variables.
We show that every closed subset of C that has finite (2N - 2)-dimensional measure is a removable set for holomorphic functions, and we obtain a related result on the ball.
A domain whose envelope of holomorphy is not a domain
We construct a domain of holomorphy in , N≥ 2, whose envelope of holomorphy is not diffeomorphic to a domain in .
Some envelopes of holomorphy
We construct some envelopes of holomorphy that are not equivalent to domains in ℂⁿ.
Polydiscs in Complex Manifolds.
On pluriharmonic interpolation.
Boundary regularity for holomorphic maps from the disc to the ball.
The ends of discs
An approximation theorem related to good compact sets in the sense of Martineau
This note contains an approximation theorem that implies that every compact subset of is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.
Strong boundary values : independence of the defining function and spaces of test functions
The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.
Corrigendum - An approximation theorem related to good compact sets in the sense of Martineau
Maximum modulus sets
We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain of dimension . If is a smooth manifold of dimension and a maximum modulus set, then it admits a unique foliation by compact interpolation manifolds. There is a semiglobal converse in the real analytic case. Two functions in with the same smooth -dimensional maximum modulus set are analytically related and are polynomially related if a certain homology class in vanishes or if is polynomially...
Regular holomorphic images of balls
Every -dimensional complex manifold (connected, paracompact and Hausdorff) is the image of the unit ball in under a finite holomorphic map that is locally biholomorphic.
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