A Discrete Hilbert Transform with Circle Packings

1. Auflage 2017
ISBN: 978-3-658-20456-3
Verlag: Springer

Buch, Englisch, 102 Seiten, Format (B × H): 148 mm x 210 mm, Gewicht: 1607 g

Reihe: BestMasters

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.

Zielgruppe

Research

Autoren/Hrsg.

Volland, Dominik

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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.

Über Autor(innen)

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