A Discrete Hilbert Transform with Circle Packings by Dominik Volland

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.

2017 | ISBN: 9783658204563