A Discrete Hilbert Transform with Circle Packings

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.

• | Author: Dominik Volland
• | Publisher: Springer Spektrum
• | Publication Date: Dec 13, 2017
• | Number of Pages: 102 pages
• | Binding: Paperback or Softback
• | ISBN-10: 3658204567
• | ISBN-13: 9783658204563