Behavior of the Carathéodory metric near strictly convex boundary points.
A method of holomorphic retractions and pseudoinverse matrices in the theory of continuation of δ-tempered functions
CONTENTS§1. Introduction.................................................................................................................5§2. Basic properties of δ-tempered holomorphic functions...............................................8§3. Holomorphic continuation and holomorphic retractions.............................................20§4. Continuation from regular neighbourhoods...............................................................32§5. Continuation from δ-regular submanifolds;...
Multiplicative linear functionals on some algebras of holomorphic functions with restricted growth
Invariant distances and metrics in complex analysis-revisited
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 .
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 note on holomorphic mappings with two fixed points
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.
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 .
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].
Geodesics for convex complex ellipsoids
On extremal holomorphically contractible families
We prove (Theorem 1.2) that the category of generalized holomorphically contractible families (Definition 1.1) has maximal and minimal objects. Moreover, we present basic properties of these extremal families.
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