A Discrete Hilbert Transform with Circle Packings

by Dominik Volland

Overview

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.

Product Details

ISBN-13:	9783658204563
Publisher:	Springer Fachmedien Wiesbaden
Publication date:	12/02/2017
Series:	BestMasters
Edition description:	1st ed. 2017
Pages:	102
Product dimensions:	5.83(w) x 8.27(h) x (d)

About the Author

Dominik Volland currently attends his postgraduate studies in the master’s program on computational science and engineering at the Technical University of Munich (TUM).

Table of Contents

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.