Perturbing Rational Harmonic Functions by Poles

@article{Ste2014PerturbingRH,
  title={Perturbing Rational Harmonic Functions by Poles},
  author={Olivier S{\`e}te and Robert Luce and J{\"o}rg Liesen},
  journal={Computational Methods and Function Theory},
  year={2014},
  volume={15},
  pages={9-35}
}
We study how adding certain poles to rational harmonic functions of the form $$R(z)-\overline{z}$$R(z)-z¯, with $$R(z)$$R(z) rational and of degree $$d\ge 2$$d≥2, affects the number of zeros of the resulting functions. Our results are motivated by and generalize a construction of Rhie derived in the context of gravitational microlensing (arXiv:astro-ph/0305166). Of particular interest is the construction and the behavior of rational functions $$R(z)$$R(z) that are extremal in the sense that $$R… Expand

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