A Discrete Hilbert Transform with Circle Packings

By Dominik Volland

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.

• Format: Paperback
• Language: English
• ISBN: 3658204567
• ISBN13: 9783658204563
• Release Date: December 2017
• Publisher: Springer Spektrum
• Length: 102 Pages
• Weight: 0.33 lbs.
• Dimensions: 0.2" x 5.8" x 8.3"