TY  - CHAP
A1  - Le, Hoai Thu
A1  - Morais, Joao
A1  - Sprößig, Wolfgang
ED  - Gürlebeck, Klaus
ED  - Lahmer, Tom
ED  - Werner, Frank
T1  - ORTHOGONAL DECOMPOSITIONS AND THEIR APPLICATIONS
T2  - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar
N2  - It is well known that complex quaternion analysis plays an important role in the study of higher order boundary value problems of mathematical physics. Following the ideas given for real quaternion analysis, the paper deals with certain orthogonal decompositions of the complex quaternion Hilbert space into its subspaces of null solutions of Dirac type operator with an arbitrary complex potential. We then apply them to consider related boundary value problems, and to prove the existence and uniqueness as well as the explicit representation formulae of the underlying solutions.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Computerunterstütztes Verfahren
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27729
UR  - http://euklid.bauing.uni-weimar.de/ikm2012
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Morais, Joao
A1  - Georgiev, Svetlin
ED  - Gürlebeck, Klaus
ED  - Lahmer, Tom
ED  - Werner, Frank
T1  - COMPLETE ORTHOGONAL SYSTEMS OF 3D SPHEROIDAL MONOGENICS
T2  - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar
N2  - In this paper we review two distint complete orthogonal systems of monogenic polynomials over 3D prolate spheroids. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with R3 and R4), and are generally assumed to be nullsolutions of the well known Riesz and Moisil Théodoresco systems in R3. This will be done in the spaces of square integrable functions over R and H. The representations of these polynomials are explicitly given. Additionally, we show that these polynomial functions play an important role in defining the Szegö kernel function over the surface of 3D spheroids. As a concrete application, we prove the explicit expression of the monogenic Szegö kernel function over 3D prolate spheroids.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Computerunterstütztes Verfahren
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27785
UR  - http://euklid.bauing.uni-weimar.de/ikm2012
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Morais, Joao
A1  - Georgiev, Svetlin
A1  - Sprößig, Wolfgang
ED  - Gürlebeck, Klaus
ED  - Lahmer, Tom
ED  - Werner, Frank
T1  - A NOTE ON THE CLIFFORD FOURIER-STIELTJES TRANSFORM
T2  - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar
N2  - The purpose of this article is to provide an overview of the real Clifford Fourier- Stieltjes transform (CFST) and of its important properties. Additionally, we introduce the definition of convolution of Clifford functions of bounded variation.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Computerunterstütztes Verfahren
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27794
UR  - http://euklid.bauing.uni-weimar.de/ikm2012
SN  - 1611-4086
ER  -