A Discrete Hilbert Transform with Circle Packings

By: Dominik Volland

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Paperback | 13 December 2017

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116 Pages

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21.01 x 14.81 x 0.61

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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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