Wyniki wyszukiwania

1

Łojasiewicz-Siciak condition for the pluricomplex Green function

100%

Kosek M.

Banach Center Publications

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2011

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tom 92

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nr 1

197-203

EN

A compact set $K ⊂ ℂ^N$ satisfies Łojasiewicz-Siciak condition if it is polynomially convex and there exist constants B,β > 0 such that $V_K(z) ≥ B(dist(z,K))^β$ if dist(z,K) ≤ 1. (LS) Here $V_K$ denotes the pluricomplex Green function of the set K. We cite theorems where this condition is necessary in the assumptions and list known facts about sets satisfying inequality (LS).

2

Some novel ways of generating Cantor and Julia type sets

100%

Kosek M.

Annales Polonici Mathematici

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2012

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tom 106

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nr 1

207-214

EN

It is a survey article showing how an enhanced version of the Banach contraction principle can lead to generalizations of attractors of iterated function systems and to Julia type sets.

3

Generalized iterated function systems, multifunctions and Cantor sets

63%

Klimek M., Kosek M.

Annales Polonici Mathematici

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2009

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tom 96

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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.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Banach Center Publications

3 Kosek M.

1 Klimek M.

1 2012

1 2011

1 2009

Łojasiewicz-Siciak condition for the pluricomplex Green function

Some novel ways of generating Cantor and Julia type sets

Generalized iterated function systems, multifunctions and Cantor sets