Dominik Volland studies the construction of a discrete counterpart
to the Hilbert transform in the realm of a nonlinear discrete
complex analysis given by circle packings. The Hilbert transform is
closely related to Riemann-Hilbert problems which have been studied
in the framework of circle packings by E. Wegert and co-workers
since 2009. The author demonstrates that the discrete Hilbert
transform is well-defined in this framework by proving a conjecture
on discrete problems formulated by Wegert. Moreover, he illustrates
its properties by carefully chosen numerical examples.
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