| 1. |
- Alghamdi, Azza, et al.
(författare)
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Probabilistic approximation of partly filled-in composite Julia sets
- 2017
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Ingår i: Annales Polonici Mathematici. - : Institute of Mathematics, Polish Academy of Sciences. - 0066-2216 .- 1730-6272. ; 119:3, s. 203-220
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Tidskriftsartikel (refereegranskat)abstract
- We study properties of the metric space of pluriregular sets and of contractions on that space induced by finite families of proper polynomial mappings of several complex variables. In particular, we show that closed balls in the space of pluriregular sets do not have to be compact and we give a simple proof of applicability of the so-called chaos game in the case of composite Julia sets. Part of the construction of those sets also leads to a computationally viable approximation by simpler sets based on Monte-Carlo simulation.
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| 2. |
- Czyz, Rafal, et al.
(författare)
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Plurisubharmonic functions on compact sets
- 2012
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Ingår i: Annales Polonici Mathematici. - : Institute of Mathematics, Polish Academy of Sciences. - 0066-2216 .- 1730-6272. ; 106, s. 133-144
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Tidskriftsartikel (refereegranskat)abstract
- Poletsky has introduced a notion of plurisubharmonicity for functions defined on compact sets in C-n. We show that these functions can be completely characterized in terms of monotone convergence of plurisubharmonic functions defined on neighborhoods of the compact.
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| 3. |
- Kiselman, Christer Oscar, Guest Professor, 1939-
(författare)
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Generalized convexity : The case of lineally convex Hartogs domains
- 2019
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Ingår i: Annales Polonici Mathematici. - : Institute of Mathematics of the Polish Academy of Sciences. - 0066-2216 .- 1730-6272. ; 123, s. 319-344
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Tidskriftsartikel (refereegranskat)abstract
- Inspired by mathematical morphology we study generalized convexity and prove that certain subsets of Hartogs domains are convex in a generalized sense.
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| 4. |
- Klimek, Maciej, et al.
(författare)
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Generalized iterated function systems, multifunctions and Cantor sets
- 2009
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Ingår i: Annales Polonici Mathematici. - Warsaw : IM PAN. - 0066-2216 .- 1730-6272. ; 96:1, s. 25-41
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Tidskriftsartikel (refereegranskat)abstract
- Using a construction similar to an iterated function system, but withfunctions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.
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| 5. |
- Klimek, Maciej
(författare)
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Personal reflections on Jozef Siciak's mathematical journey
- 2019
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Ingår i: Annales Polonici Mathematici. - : POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN. - 0066-2216 .- 1730-6272. ; 123:1, s. 1-7
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Tidskriftsartikel (refereegranskat)abstract
- The recent passing of Professor Jozef Siciak inevitably brings about reflections on his legacy, not just in terms of mathematical results he had obtained or inspired, but also in terms of shaping the way mathematics is being developed internally and as a part of science in general. Based on several decades of close personal contacts, the author attempts to outline Professor Siciak's views concerning these matters.
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| 6. |
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