A Discrete Hilbert Transform with Circle Packings

• Main Author: Volland, Dominik (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Wiesbaden : Springer Fachmedien Wiesbaden : Imprint: Springer Spektrum, 2017.
• Series: BestMasters
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Computer mathematics.; Geometry.; Analysis.; Computational Mathematics and Numerical Analysis.

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...

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.