TY  - CHAP
A1  - Franssens, Ghislain R.
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - INTRODUCTION TO CLIFFORD ANALYSIS OVER PSEUDO-EUCLIDEAN SPACE
N2  - An introduction is given to Clifford Analysis over pseudo-Euclidean space of arbitrary signature, called for short Ultrahyperbolic Clifford Analysis (UCA). UCA is regarded as a function theory of Clifford-valued functions, satisfying a first order partial differential equation involving a vector-valued differential operator, called a Dirac operator. The formulation of UCA presented here pays special attention to its geometrical setting. This permits to identify tensors which qualify as geometrically invariant Dirac operators and to take a position on the naturalness of contravariant and covariant versions of such a theory. In addition, a formal method is described to construct the general solution to the aforementioned equation in the context of covariant UCA.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
KW  - Computerunterstütztes Verfahren
KW  - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28433
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  -