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1
Content available A method of holomorphic retractions and pseudoinverse matrices in the theory of continuation of δ-tempered functions
100%
Jarnicki M.
Instytut Matematyczny Polskiej Akademii Nauk
EN
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; Main Theorem........................................35 §6. Holomorphic retractions and pseudoinverse matrices; proof of Main Theorem.........39 References.....................................................................................................................49
2
Content available remote Invariant pseudodistances and pseudometrics - completeness and product property
58%
Jarnicki M. , Pflug P.
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1991
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tom 55
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nr 1
169-189
EN
A survey of properties of invariant pseudodistances and pseudometrics is given with special stress put on completeness and product property.
3
Content available remote Cross theorem
58%
Jarnicki M. , Pflug P.
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2001
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tom 77
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nr 3
295-302
EN
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].
4
Content available remote New examples of effective formulas for holomorphically contractible functions
58%
Jarnicki M. , Pflug P.
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nr 3
219-230
EN
Let $G ⊂ ℂ^n$ and $B ⊂ ℂ^m$ 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.
5
Content available remote A remark on the identity principle for analytic sets
58%
Jarnicki M. , Pflug P.
Colloquium Mathematicum
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2011
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tom 123
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nr 1
21-26
EN
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.
6
Content available remote On balanced L²-domains of holomorphy
58%
Jarnicki M. , Pflug P.
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nr 1
101-102
EN
We show that any bounded balanced domain of holomorphy is an $L²_h$-domain of holomorphy.
7
Content available remote A remark on separate holomorphy
58%
Jarnicki M. , Pflug P.
Studia Mathematica
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2006
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tom 174
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nr 3
309-317
EN
Let X be a Riemann domain over $ℂ^{k} × ℂ^{ℓ}$. If X is a domain of holomorphy with respect to a family ℱ ⊂𝓞(X), then there exists a pluripolar set $P ⊂ ℂ^{k}$ such that every slice $X_{a}$ of X with a∉ P is a region of holomorphy with respect to the family ${f|_{X_{a}}: f ∈ ℱ}$.
8
Content available remote An extension theorem for separately holomorphic functions with analytic singularities
58%
Jarnicki M. , Pflug P.
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2003
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tom 80
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nr 1
143-161
EN
Let $D_j ⊂ ℂ^{k_j}$ be a pseudoconvex domain and let $A_j ⊂ D_j$ be a locally pluriregular set, j = 1,...,N. Put $X: = ⋃_{j=1}^N A₁ ×. .. × A_{j-1} × D_j × A_{j+1} ×. .. × A_N ⊂ ℂ^{k₁+...+k_N}$. 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 $f̂|_{X∖M} = f$. The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001].
9
Content available remote On extremal holomorphically contractible families
47%
Jarnicki M. , Jarnicki W. , Pflug P.
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2003
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tom 81
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nr 2
183-199
EN
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.
10
Content available A note on holomorphic mappings with two fixed points
41%
Jarnicki M. , Tworzewski P.
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nr 1
179-182
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