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Volland, Dominik

 
9783658204563: A Discrete Hilbert Transform with Circle Packings

Synopsis

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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À propos de l'auteur

Dominik Volland currently attends his postgraduate studies in the master's program on computational science and engineering at the Technical University of Munich (TUM).

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