TY - JOUR
T1 - On the Moisil-Theodoresco Operator in Orthogonal Curvilinear Coordinates
AU - Bory Reyes, J.
AU - Pérez-de la Rosa, M. A.
N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/3
Y1 - 2021/3
N2 - The action of the Moisil-Theodoresco operator over a quaternionic valued function defined on R3 (sum of a scalar and a vector field) in Cartesian coordinates is generally well understood. However this is not the case for any orthogonal curvilinear coordinate system. This paper sheds some new light on the technical aspect of the subject. Moreover, we introduce a notion of quaternionic Laplace operator acting on a quaternionic valued function from which one can recover both scalar and vector Laplacians in the vector analysis context.
AB - The action of the Moisil-Theodoresco operator over a quaternionic valued function defined on R3 (sum of a scalar and a vector field) in Cartesian coordinates is generally well understood. However this is not the case for any orthogonal curvilinear coordinate system. This paper sheds some new light on the technical aspect of the subject. Moreover, we introduce a notion of quaternionic Laplace operator acting on a quaternionic valued function from which one can recover both scalar and vector Laplacians in the vector analysis context.
KW - Laplace operator
KW - Moisil-Theodoresco operator
KW - hyperholomorphic functions
KW - orthogonal curvilinear coordinates
UR - http://www.scopus.com/inward/record.url?scp=85084519397&partnerID=8YFLogxK
U2 - 10.1007/s40315-020-00319-8
DO - 10.1007/s40315-020-00319-8
M3 - Artículo
AN - SCOPUS:85084519397
SN - 1617-9447
VL - 21
SP - 131
EP - 144
JO - Computational Methods and Function Theory
JF - Computational Methods and Function Theory
IS - 1
ER -