Ebook: A Discrete Hilbert Transform with Circle Packings (BestMasters)
Author: Dominik Volland
- Tags: Mathematics, Calculus, Complex variable
- Series: BestMasters
- Year: 2017
- Publisher: Springer Spektrum
- Edition: 1st ed. 2017
- Language: English
- pdf
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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