TY - JOUR
T1 - Cauchy Integral Formulae in Quaternionic Hermitean Clifford Analysis
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Brackx, Fred
AU - de Schepper, Hennie
AU - Sommen, Frank
PY - 2012/10
Y1 - 2012/10
N2 - The theory of complex Hermitean Clifford analysis was developed recently as a refinement of Euclidean Clifford analysis; it focusses on the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean Dirac operators constituting a splitting of the traditional Dirac operator. In this function theory, the fundamental integral representation formulae, such as the Borel-Pompeiu and the Clifford-Cauchy formula have been obtained by using a (2 × 2) circulant matrix formulation. In the meantime, the basic setting has been established for so-called quaternionic Hermitean Clifford analysis, a theory centred around the simultaneous null solutions, called q-Hermitean monogenic functions, of four Hermitean Dirac operators in a quaternionic Clifford algebra setting. In this paper we address the problem of establishing a quaternionic Hermitean Clifford-Cauchy integral formula, by following a (4 × 4) circulant matrix approach.
AB - The theory of complex Hermitean Clifford analysis was developed recently as a refinement of Euclidean Clifford analysis; it focusses on the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean Dirac operators constituting a splitting of the traditional Dirac operator. In this function theory, the fundamental integral representation formulae, such as the Borel-Pompeiu and the Clifford-Cauchy formula have been obtained by using a (2 × 2) circulant matrix formulation. In the meantime, the basic setting has been established for so-called quaternionic Hermitean Clifford analysis, a theory centred around the simultaneous null solutions, called q-Hermitean monogenic functions, of four Hermitean Dirac operators in a quaternionic Clifford algebra setting. In this paper we address the problem of establishing a quaternionic Hermitean Clifford-Cauchy integral formula, by following a (4 × 4) circulant matrix approach.
KW - Cauchy integral formula
KW - Quaternionic Hermitean Clifford analysis
UR - http://www.scopus.com/inward/record.url?scp=84867891102&partnerID=8YFLogxK
U2 - 10.1007/s11785-011-0168-8
DO - 10.1007/s11785-011-0168-8
M3 - Artículo
SN - 1661-8254
VL - 6
SP - 971
EP - 985
JO - Complex Analysis and Operator Theory
JF - Complex Analysis and Operator Theory
IS - 5
ER -