8 papers · 1 filter
Blaschke Products Sharing a Welding Homeomorphism
Kirill Lazebnik
Given two Blaschke products , of the same degree, a \emph{welding homeomorphism} of , is a circle homeomorphism satisfying $A\c…
Sharp bounds for the valence of certain logharmonic polynomials
Kirill Lazebnik, Erik Lundberg
Consider a logharmonic polynomial; that is, a product of the form , where , are holomorphic polynomials. Assume is linear and denote by the degr…
Rational lemniscates and the matching problem
Kirill Lazebnik, Pierre-Olivier Parisé, Malik Younsi
The matching problem for a given Jordan curve in the complex plane asks to find two nonconstant functions, one analytic in the bounded complementary component of the curve and the…
On the Shapes of Rational Lemniscates
Christopher J. Bishop, Alexandre Eremenko, Kirill Lazebnik
A rational lemniscate is a level set of where is rational. We prove that any planar Euler graph can be approximated, in a s…
Analytic and Topological Nets
Kirill Lazebnik
We characterize which planar graphs arise as the pullback, under a rational map , of an analytic Jordan curve passing through the critical values of . We also prove that such…
A Geometric Approach to Polynomial and Rational Approximation
Christopher J. Bishop, Kirill Lazebnik
We strengthen the classical approximation theorems of Weierstrass, Runge and Mergelyan by showing the polynomial and rational approximants can be taken to have a simple geometric s…