A Characterization of C(X) Among Algebras on Planar Sets by the Existence of a Finite Universal Korovkin System.
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.
An Increasing Sequence of Stein Manifolds whose Limit is not Stein.
An open mapping theorem for analytic multifunctions
The paper gives sufficient conditions for projections of certain pseudoconcave sets to be open. More specifically, it is shown that the range of an analytic set-valued function whose values are simply connected planar continua is open, provided there does not exist a point which belongs to boundaries of all the fibers. The main tool is a theorem on existence of analytic discs in certain polynomially convex hulls, obtained earlier by the author.
Analytic disks with boundaries in a maximal real submanifold of
Let be a two dimensional totally real submanifold of class in . A continuous map of the closed unit disk into that is holomorphic on the open disk and maps its boundary into is called an analytic disk with boundary in . Given an initial immersed analytic disk with boundary in , we describe the existence and behavior of analytic disks near with boundaries in small perturbations of in terms of the homology class of the closed curve in . We also prove a regularity theorem...
Approximation of biholomorphic mappings by automorphisms of Cn (Erratum).
Approximation of biholomorphic mappings by automorphisms of Cn.
Approximation on a disk I.
Approximation on a disk II.
Bernstein quasianalytic functions on algebraic sets.
Calculus inequalities derived from holomorphic Morse inequalities.
Canvexité rationnelle des surfaces lagrangiennes.
Compact subsets of preserving Markov’s inequality
Complete pluripolar graphs in
Let F be the Cartesian product of N closed sets in ℂ. We prove that there exists a function g which is continuous on F and holomorphic on the interior of F such that is complete pluripolar in . Using this result, we show that if D is an analytic polyhedron then there exists a bounded holomorphic function g such that is complete pluripolar in . These results are high-dimensional analogs of the previous ones due to Edlund [Complete pluripolar curves and graphs, Ann. Polon. Math. 84 (2004), 75-86]...
Corrigendum - An approximation theorem related to good compact sets in the sense of Martineau
Domains of biregularity in Clifford analysis
Eine geometrische Eigenschaft von Rungeschen Gebieten.
Ensembles fermés polynomialement convexes
Envelopes of Holomorphy and Polynomial Hulls.
Enveloppes polynomiales de variétés réelles dans C2.
We present here three examples concerning polynomial hulls of some manifolds in C2.1. Some real surfaces with equation w = P (z,z') + G(z) where P is a homogeneous polynomial of degree n and G(z) = o(|z|n) at 0 which are locally polynomially convex at 0.2. Some real surfaces MF with equation w = zn+kz'n + F(z,z') such that the hull of Mf ∩ B'(0,1) contains a neighbourhood of 0.3. A contable union of totally real planes (Pj) such that B'(0,1) ∩ (∪j∈N Pj) is polynomially convex.