Quadratintegrable holomorphe Funktionen und die Serre-Vermutung.
Über polynomiale Funktionen auf Holomorphiegebieten.
Extension of separately holomorphic functions-a survey 1899-2001
This note is an attempt to describe a part of the historical development of the research on separately holomorphic functions.
Invariant distances and metrics in complex analysis-revisited
Über Gebiete mit vollständiger Kählermetrik.
On the extended tube conjecture.
The inner Carathédory distance for the annulus.
On n-circled -domains of holomorphy
We present various characterizations of n-circled domains of holomorphy with respect to some subspaces of .
Effective formulas for invariant functions - case of elementary Reinhardt domains
We find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the functions are calculated explicitly.
Erratum to "Effective formulas for invariant functions - case of elementary Reinhardt domains" (Ann. Polon. Math. 69 (1998), 175-196)
On balanced L²-domains of holomorphy
We show that any bounded balanced domain of holomorphy is an -domain of holomorphy.
Invariant pseudodistances and pseudometrics - completeness and product property
A survey of properties of invariant pseudodistances and pseudometrics is given with special stress put on completeness and product property.
New examples of effective formulas for holomorphically contractible functions
Let and be domains and let Φ:G → B be a surjective holomorphic mapping. We characterize some cases in which invariant functions and pseudometrics on G can be effectively expressed in terms of the corresponding functions and pseudometrics on B.
A remark on the identity principle for analytic sets
We present a version of the identity principle for analytic sets, which shows that the extension theorem for separately holomorphic functions with analytic singularities follows from the case of pluripolar singularities.
-domains of holomorphy and the Bergman kernel
We give a characterization of -domains of holomorphy with the help of the boundary behavior of the Bergman kernel and geometric properties of the boundary, respectively.
A remark on separate holomorphy
Let X be a Riemann domain over . If X is a domain of holomorphy with respect to a family ℱ ⊂(X), then there exists a pluripolar set such that every slice of X with a∉ P is a region of holomorphy with respect to the family .
Local vs. global hyperconvexity, tautness or -completeness for unbounded open sets in
Some known localization results for hyperconvexity, tautness or -completeness of bounded domains in are extended to unbounded open sets in .
The Serre problem with Reinhardt fibers
The Serre problem is solved for fiber bundles whose fibers are two-dimensional pseudoconvex hyperbolic Reinhardt domains.
An extension theorem for separately holomorphic functions with analytic singularities
Let be a pseudoconvex domain and let be a locally pluriregular set, j = 1,...,N. Put . Let U be an open connected neighborhood of X and let M ⊊ U be an analytic subset. Then there exists an analytic subset M̂ of the “envelope of holomorphy” X̂ of X with M̂ ∩ X ⊂ M such that for every function f separately holomorphic on X∖M there exists an f̂ holomorphic on X̂∖M̂ with . The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001].
Cross theorem
Let D,G ⊂ ℂ be domains, let A ⊂ D, B ⊂ G be locally regular sets, and let X:= (D×B)∪(A×G). Assume that A is a Borel set. Let M be a proper analytic subset of an open neighborhood of X. Then there exists a pure 1-dimensional analytic subset M̂ of the envelope of holomorphy X̂ of X such that any function separately holomorphic on X∖M extends to a holomorphic function on X̂ ∖M̂. The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], and [Sic 2000].
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