401 citations · 571 across the 24 of their papers we have counts for
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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…
Walsh's conformal map onto lemniscatic domains for polynomial pre-images I
Klaus Schiefermayr, Olivier Sète
We consider Walsh's conformal map from the exterior of a compact set onto a lemniscatic domain. If is simply connected, the lemniscatic domain is the e…
Minimal degree rational open up mappings and related questions
Sergei Kalmykov, Béla Nagy, Olivier Sète
We establish the existence and uniqueness of rational conformal maps of minimal degree for opening up arcs. In earlier results, the degree was exponential in . We also…
Number and location of pre-images under harmonic mappings in the plane
Olivier Sète, Jan Zur
We derive a formula for the number of pre-images under a non-degenerate harmonic mapping , using the argument principle. This formula reveals a connection between the pre-images…
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…
The index of singular zeros of harmonic mappings of anti-analytic degree one
Robert Luce, Olivier Sète
We study harmonic mappings of the form , where is an analytic function. In particular we are interested in the index (a generalized multiplicity) of…
Numerical computation of the conformal map onto lemniscatic domains
Mohamed M. S. Nasser, Jörg Liesen, Olivier Sète
We present a numerical method for the computation of the conformal map from unbounded multiply-connected domains onto lemniscatic domains. For -times connected domains the me…
Properties and examples of Faber--Walsh polynomials
Olivier Sète, Jörg Liesen
The Faber--Walsh polynomials are a direct generalization of the (classical) Faber polynomials from simply connected sets to sets with several simply connected components. In this p…
On conformal maps from multiply connected domains onto lemniscatic domains
Olivier Sète, Jörg Liesen
We study conformal maps from multiply connected domains in the extended complex plane onto lemniscatic domains. Walsh proved the existence of such maps in 1956 and thus obtained a…
A Note on the Maximum Number of Zeros of
Robert Luce, Olivier Sète, Jörg Liesen
An important theorem of Khavinson & Neumann (Proc. Amer. Math. Soc. 134(4), 2006) states that the complex harmonic function , where is a rational function of de…
Perturbing rational harmonic functions by poles
Olivier Sète, Robert Luce, Jörg Liesen
We study how adding certain poles to rational harmonic functions of the form , with rational and of degree , affects the number of zeros of the result…
Some properties of Faber-Walsh polynomials
Olivier Sète
Walsh introduced a generalisation of Faber polynomials to certain compact sets which need not be connected. We derive several equivalent representations of these Faber-Walsh polyno…