74 citations · 255 across the 21 of their papers we have counts for
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The maximum number of zeros of revisited
Jörg Liesen, Jan Zur
Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions $f(z) = \frac{p(z)}{q(z)} - \ov…
How constant shifts affect the zeros of certain rational harmonic functions
Jörg Liesen, Jan Zur
We study the effect of constant shifts on the zeros of rational harmomic functions $f(z) = r(z) - \conj{z}$. In particular, we characterize how shifting through the caustics 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…
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…