10 citations · 36 across the 6 of their papers we have counts for
6 papers
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…
The transport of images method: computing all zeros of harmonic mappings by continuation
Olivier Sète, Jan Zur
We present a continuation method to compute all zeros of a harmonic mapping in the complex plane. Our method works without any prior knowledge of the number of zeros or their a…
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 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 …