5 papers · 1 filter
The Complex Green's Function for Symmetric Sets
Klaus Schiefermayr, Olivier Sète
The aim of this paper is threefold: (i) We study the complex Green's function (the analytic extension of the real Green's function) for multiply connected domains with some symmetr…
On the zeros of polyanalytic polynomials
Olivier Sète, Jan Zur
We give sufficient conditions under which a polyanalytic polynomial of degree has (i) at least one zero, and (ii) finitely many zeros. In the latter case, we prove that the num…
Walsh's Conformal Map onto Lemniscatic Domains for Several Intervals
Klaus Schiefermayr, Olivier Sète
We consider Walsh's conformal map from the complement of a compact set with components onto a lemniscatic domain …
Walsh's Conformal Map onto Lemniscatic Domains for Polynomial Pre-images II
Klaus Schiefermayr, Olivier Sète
We consider Walsh's conformal map from the exterior of a set consisting of compact disjoint components onto a lemniscatic domain. In particular, w…
A Newton method for harmonic mappings in the plane
Olivier Sète, Jan Zur
We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation…