On the Moisil-Theodoresco Operator in Orthogonal Curvilinear Coordinates

The action of the Moisil-Theodoresco operator over a quaternionic valued function defined on R 3 (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...

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Bibliographic Details
Published in:Computational methods and function theory 2021-03, Vol.21 (1), p.131-144
Main Authors: Bory Reyes, J., Pérez-de la Rosa, M. A.
Format: Article
Language:English
Subjects:
Analysis
Cartesian coordinates
Computational Mathematics and Numerical Analysis
Fields (mathematics)
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Spherical coordinates
Vector analysis
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Summary:The action of the Moisil-Theodoresco operator over a quaternionic valued function defined on R 3 (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.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-020-00319-8