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Invariant pluricomplex Green functions

100%
Klimek M.
Banach Center Publications
|
1995
|
tom 31
|
nr 1
207-226
EN
The purpose of this paper is to present a concise survey of the main properties of biholomorphically invariant pluricomplex Green functions and to describe a number of new examples of such functions. A concept of pluricomplex geodesics is also discussed.
2
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On perturbations of pluriregular sets generated by sequences of polynomial maps

100%
Klimek M.
Annales Polonici Mathematici
|
2003
|
tom 80
|
nr 1
171-184
EN
It is shown that an infinite sequence of polynomial mappings of several complex variables, with suitable growth restrictions, determines a filled-in Julia set which is pluriregular. Such sets depend continuously and analytically on the generating sequences, in the sense of pluripotential theory and the theory of set-valued analytic functions, respectively.
3
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Stochastic characterization of plurisubharmonicity and convexity of functions

100%
Klimek M.
Banach Center Publications
|
2015
|
tom 107
|
nr 1
175-181
EN
It is described how both plurisubharmonicity and convexity of functions can be characterized in terms of simple to work with classes of holomorphic martingales, namely a class of driftless Itô processes satisfying a skew-symmetry property and a family of linear modifications of Brownian motion parametrized by a compact set.
4
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Generalized iterated function systems, multifunctions and Cantor sets

63%
Klimek M., Kosek M.
Annales Polonici Mathematici
|
2009
|
tom 96
|
nr 1
25-41
EN
Using a construction similar to an iterated function system, but with functions 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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