About this book
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. Basic knowledge of complex analysis and functional analysis is recommended.
- Hardy Spaces and Riemann-Hilbert Problems
- The Hilbert Transform in the Classical Setting
- Circle Packings
- Discrete Boundary Value Problems
- Discrete Hilbert Transform
- Numerical Results of Test Computations
- Properties of the Discrete Transform
Lecturers and students of mathematics who are interested in circle packings and/or discrete Riemann-Hilbert problems
Dominik Volland currently attends his postgraduate studies in the master’s program on computational science and engineering at the Technical University of Munich (TUM).
circle packings Hilbert transform Riemann-Hilbert problem boundary value problem discrete analytic functions discrete complex analysis