TY  - CHAP
A1  - Cacao, Isabel
T1  - Constructive Aspects of Monogenic Function Theory
N2  - As it is well known, the approximation theory of complex valued functions is one of the main fields in function theory. In general, several aspects of approximation and interpolation are only well understood by using methods of complex analysis. It seems natural to extend these techniques to higher dimensions by using Clifford Analysis methods or, more specific, in lower dimensions 3 or 4, by using tools of quaternionic analysis. One starting point for such attempts has to be the suitable choice of complete orthonormal function systems that should replace the holomorphic function systems used in the complex case. The aim of our contribuition is the construction of a complete orthonormal system of monogenic polynomials derived from a harmonic function system by using sistematically the generalized quaternionic derivative
KW  - Komplexe Funktion
KW  - Quaternion
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-2848
ER  - 
TY  - CHAP
A1  - Cacao, Isabel
A1  - Constales, Denis
A1  - Kraußhar, Rolf Sören
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - A UNIFIED APPROACH FOR THE TREATMENT OF SOME HIGHER DIMENSIONAL DIRAC TYPE EQUATIONS ON SPHERES
N2  - Using Clifford analysis methods, we provide a unified approach to obtain explicit solutions of some partial differential equations combining the n-dimensional Dirac and Euler operators, including generalizations of the classical time-harmonic Maxwell equations. The obtained regular solutions show strong connections between hypergeometric functions and homogeneous polynomials in the kernel of the Dirac operator.
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:wim2-20170314-28343
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Cacao, Isabel
A1  - Constales, Denis
A1  - Kraußhar, Rolf Sören
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - BESSEL FUNCTIONS AND HIGHER DIMENSIONAL DIRAC TYPE EQUATIONS
N2  - In this paper we study the structure of the solutions to higher dimensional Dirac type equations generalizing the known λ-hyperholomorphic functions, where λ is a complex parameter. The structure of the solutions to the system of partial differential equations (D- λ) f=0 show a close connection with Bessel functions of first kind with complex argument. The more general system of partial differential equations that is considered in this paper combines Dirac and Euler operators and emphasizes the role of the Bessel functions. However, contrary to the simplest case, one gets now Bessel functions of any arbitrary complex order.
KW  - Architektur <Informatik>
KW  - CAD
KW  - Computerunterstütztes Verfahren
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29366
UR  - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER  -