TY - JOUR
T1 - Hypermonogenic solutions and plane waves of the Dirac operator in Rp×Rq
AU - Guzmán Adán, Alí
AU - Orelma, Heikki
AU - Sommen, Franciscus
PY - 2019/4/1
Y1 - 2019/4/1
N2 - In this paper we first define hypermonogenic solutions of the Dirac operator in Rp×Rq and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function class in classical Clifford analysis. After that, we define the corresponding hypermonogenic plane wave solutions and deduce explicit methods to compute these functions.
AB - In this paper we first define hypermonogenic solutions of the Dirac operator in Rp×Rq and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function class in classical Clifford analysis. After that, we define the corresponding hypermonogenic plane wave solutions and deduce explicit methods to compute these functions.
KW - Cauchy's formula
KW - Hypermonogenic solution
KW - Plane wave
U2 - 10.1016/j.amc.2018.09.058
DO - 10.1016/j.amc.2018.09.058
M3 - Article
VL - 346
SP - 1
EP - 14
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
ER -