Seminar Event Detail


Complex Analysis, Dynamics and Geometry

Date:  Monday, March 05, 2018
Location:  3096 East Hall (12:00 AM to 12:00 AM)

Title:  Pseudo-Leja points and approximation of planar sets by polynomial Julia sets

Abstract:   We revisit approximation of nonempty compact planar sets by filled-in Julia sets of polynomials proposed by K. Lindsey and M. Younsi and connect it with recent results in interpolation theory by V. Andrievskii, M. Ounaies, A. Irigoyen and others. Specifically, we show that using slightly modified fundamental Lagrange interpolation polynomials with certain nodes having subexponential growth of Lebesgue constants improves the approximation rate given by Lindsey and Younsi. To this end we investigate interpolation properties of some arrays of points in $\mathbb{C}$ and 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. This is joint work with Leokadia Bialas-Ciez and Marta Kosek.

Files:


Speaker:  Margaret Stawiska-Friedland
Institution:  Math Reviews

Event Organizer:     

 

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