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Łojasiewicz-Siciak condition for the pluricomplex Green function

100%

Kosek M.

Banach Center Publications

2011

tom 92

nr 1

197-203

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).

A few facts concerning the outstanding Polish mathematician Franciszek Leja

100%

Kosek M.

We present a collection of facts given by the outstanding Polish mathematician Franciszek Leja (1885‒1979) in his unpublished memoirs, add some other information about him and list some institutions bearing his name.

Some novel ways of generating Cantor and Julia type sets

100%

Kosek M.

Annales Polonici Mathematici

2012

tom 106

nr 1

207-214

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.

Generalized iterated function systems, multifunctions and Cantor sets

63%

Klimek M. , Kosek M.

Annales Polonici Mathematici

2009

tom 96

nr 1

25-41

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.