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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Vydáno v:Computational methods and function theory Ročník 21; číslo 1; s. 131 - 144
Hlavní autoři: Bory Reyes, J., Pérez-de la Rosa, M. A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2021
Springer Nature B.V
Témata:
Analysis
Cartesian coordinates
Computational Mathematics and Numerical Analysis
Fields (mathematics)
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Spherical coordinates
Vector analysis
Laplace operator
Primary 30G35
Moisil-Theodoresco operator
hyperholomorphic functions
orthogonal curvilinear coordinates
Secondary 35J05
ISSN:1617-9447, 2195-3724
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-020-00319-8