Dominik Volland

A Discrete Hilbert Transform with Circle Packings (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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
• Propertiesof the Discrete Transform

Target Groups

Lecturers and students of mathematics who are interested in circle packings and/or discrete Riemann-Hilbert problems

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).

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Produktdetails

• Verlag: Springer Fachmedien Wiesbaden
• Seitenzahl: 102
• Erscheinungstermin: 1. Dezember 2017
• Englisch
• ISBN-13: 9783658204570
• Artikelnr.: 53062058

Autorenporträt

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

Inhaltsangabe

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.