Refine
Document Type
- Conference Proceeding (286)
- Article (3)
Institute
- In Zusammenarbeit mit der Bauhaus-Universität Weimar (174)
- Graduiertenkolleg 1462 (31)
- Professur Informatik im Bauwesen (24)
- Institut für Strukturmechanik (ISM) (22)
- Professur Angewandte Mathematik (18)
- Institut für Konstruktiven Ingenieurbau (IKI) (8)
- Professur Stahlbau (4)
- Institut für Bauinformatik, Mathematik und Bauphysik (IBMB) (3)
- Professur Informatik in der Architektur (3)
- Professur Stochastik und Optimierung (3)
Keywords
- Computerunterstütztes Verfahren (289) (remove)
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.