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1
Content available remote

Holomorphic motions commuting with semigroups

100%
Słodkowski Z.
Studia Mathematica
|
1996
|
tom 119
|
nr 1
1-16
EN
A holomorphic family $f_z$, |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms $F_z$, |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions $F_z$ which, in addition, commute with some holomorphic families of holomorphic endomorphisms of $ℂ̅̅̅̅̅̅ \ f_z(E)$, |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.
2
Content available remote

Polynomially convex hulls of families of arcs

100%
Słodkowski Z.
Studia Mathematica
|
2004
|
tom 165
|
nr 1
1-17
EN
The paper is devoted to the study of polynomially convex hulls of compact subsets of ℂ², fibered over the boundary of the unit disc, such that all fibers are simple arcs in the plane and their endpoints form boundaries of two closed, not intersecting analytic discs. The principal question concerned is under what additional condition such a hull is a bordered topological hypersurface and, in particular, is foliated by a unique holomorphic motion. One of the main results asserts that this happens when the family of arcs satisfies the Continuous Cone Condition.
3
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An open mapping theorem for analytic multifunctions

100%
Słodkowski Z.
Studia Mathematica
|
1997
|
tom 122
|
nr 2
117-122
EN
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.
4
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On ideals consisting of joint topological divisors of zero

38%
Słodkowski Z.
Studia Mathematica
|
1973
|
tom 48
|
nr 1
83-88
5
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A criterion for subharmonicity of a function of the spectrum

32%
Słodkowski Z.
Studia Mathematica
|
1982-1983
|
tom 75
|
nr 1
37-49
6
Content available remote

An infinite family of joint spectra

26%
Słodkowski Z.
Studia Mathematica
|
1977
|
tom 61
|
nr 3
239-255
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