TY  - CONF
A1  - Vieira, Nelson
A2  - Gürlebeck, Klaus
A2  - Lahmer, Tom
T1  - SOME RESULTS IN FRACTIONAL CLIFFORD ANALYSIS
T2  - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
N2  - What is nowadays called (classic) Clifford analysis consists in the establishment of a function theory for functions belonging to the kernel of the Dirac operator. While such functions can very well describe problems of a particle with internal SU(2)-symmetries, higher order symmetries are beyond this theory. Although many modifications (such as Yang-Mills theory) were suggested over the years they could not address the principal problem, the need of a n-fold factorization of the d’Alembert operator. In this paper we present the basic tools of a fractional function theory in higher dimensions, for the transport operator (alpha = 1/2 ), by means of a fractional correspondence to the Weyl relations via fractional Riemann-Liouville derivatives. A Fischer decomposition, fractional Euler and Gamma operators, monogenic projection, and basic fractional homogeneous powers are constructed.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Building Information Modeling
KW  - Computerunterstütztes Verfahren
KW  - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications
Y1  - 2015
UR  - https://e-pub.uni-weimar.de/opus4/frontdoor/index/index/docId/2825
UR  - https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-28256
SN  - 1611-4086
ER  -