Marta Kosek

Hölder continuity property of filled-in Julia sets in {ℂ}ⁿ

It is proved that the pluricomplex Green function of the filled-in Julia set J associated with a polynomial mapping in Cn is Hölder continuous. This yields in particular that J preserves Markov’s inequality.

Iteration of polynomial mappings on algebraic sets

In this paper we consider algebraic sets M and polynomial mappings P such that P(M)⊂M. We establish Hölder type estimates on the set M for the L-extremal function of the portion K[P]∩ M, where K[P] is the filled-in Julia set associated with P. We also give someexamples of sets preserving tangential Markov type inequality

On Lagrange polynomials and the rate of approximation of planar sets by polynomial Julia sets

Abstract We revisit the approximation of nonempty compact planar sets by filled-in Julia sets of polynomials developed in [27] and analyze the rate of approximation. We use slightly modified fundamental Lagrange interpolation polynomials and show that taking certain classes of nodes with subexponential growth of Lebesgue constants improves the approximation rate. To this end we investigate properties of some arrays of points in C . In particular we prove subexponential growth of Lebesgue constants for pseudo Leja sequences with bounded Edrei growth on finite unions of quasiconformal arcs. Finally, for some classes of sets we estimate more precisely the rate of approximation by filled-in Julia sets in Hausdorff and Klimek metrics.

A few facts concerning the outstanding Polish mathematician Franciszek Leja

We present a collection of facts given by the outstanding Polish mathematician Franciszek Leja (1885‒1979) in his unpublished memoirs, add some other information about him and list some institutions bearing his name.