The Hermitian Clifford Analysis Toolbox

• DOI: 10.1007/s00006-008-0081-z
• Publication Date: 2008-04-26T03:41:36Z
• Authors: Fred Brackx; Hennie De Schepper; Frank Sommen
• Keywords: 0101 mathematics; 01 natural sciences

Hermitian Clifford analysis focusses on monogenic functions taking values in a complex Clifford algebra or in a complex spinor space. Here monogenicity is expressed by means of two complex mutually adjoint Dirac operators, which are invariant under the action of a representation of the unitary group. In this paper we have properly developed the Hermitian Clifford analysis framework and established a Hermitian Fischer decomposition, which, as is the case in traditional Clifford analysis, is a corner stone of the function theory.