A Discrete Hilbert Transform with Circle Packings (BestMasters)

A Discrete Hilbert Transform with Circle Packings (BestMasters)

Author
Dominik Volland
Publisher
Springer Spektrum
Language
English
Edition
1st ed. 2017
Year
2017
Page
116
ISBN
3658204567,9783658204563
File Type
pdf
File Size
1.6 MiB

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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