A Discrete Hilbert Transform with Circle Packings

✍ Scribed by Dominik Volland (auth.)

• Publisher: Springer Spektrum
• Year: 2017
• Tongue: English
• Leaves: 110
• Series: BestMasters
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xi
Introduction (Dominik Volland)....Pages 1-2
Auxiliary Material and Notation (Dominik Volland)....Pages 3-7
The Continuous Setting (Dominik Volland)....Pages 9-34
Circle Packings (Dominik Volland)....Pages 35-60
Discrete Hilbert Transform (Dominik Volland)....Pages 61-88
Numerical Results and Future Work (Dominik Volland)....Pages 89-99
Back Matter ....Pages 101-102

✦ Subjects

Analysis