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A Discrete Hilbert Transform with Circle Packings
Paperback
Series: Bestmasters
ISBN13: 9783658204563
Publisher: Springer Spektrum
Published: Dec 13 2017
Pages: 102
Weight: 0.33
Height: 0.24 Width: 5.83 Depth: 8.27
Language: English
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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