Title: Constructing 3D mappings onto the unit sphere with the hypercomplex Szego kernel
Authors: Constales, Denis
Grob, Dennis ×
Krausshar, Rolf Sören #
Issue Date: Apr-2010
Publisher: Elsevier
Series Title: Journal of Computational and Applied Mathematics vol:233 issue:11 pages:2884-2901
Abstract: In classical complex analysis the Szeg\"o kernel
method provides an explicit way to construct conformal maps from a given simply-connected domain $G \subset \mathbb{C}$ onto the unit disc. In this paper we revisit this method in the
three-dimensional case. We investigate whether it is possible to construct 3D mappings from some elementary domains into the three dimensional unit ball by using the hypercomplex Szeg\"o kernel. In the cases of rectangular domains, L-shaped domains, cylinders and the symmetric double-cone the proposed method leads surprisingly to qualitatively very good results. In the case of the cylinder we get even better results than those obtained by the hypercomplex Bergman method that was very recently proposed by several authors.

We round off with also giving an explicit example of a domain, namely the T-piece, where the method does not lead to the desired result. This shows that one has to adapt the methods in accordance to different classes of domains.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

Files in This Item:

There are no files associated with this item.

Request a copy


All items in Lirias are protected by copyright, with all rights reserved.

© Web of science