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On the Moisil-Theodoresco Operator in Orthogonal Curvilinear Coordinates

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Abstract

The action of the Moisil-Theodoresco operator over a quaternionic valued function defined on \({\mathbb {R}}^3\) (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.

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Acknowledgements

The authors were partially supported by Instituto Politécnico Nacional in the framework of SIP programs and by Fundación Universidad de las Américas Puebla, respectively.

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  1. ESIME-Zacatenco, Instituto Politécnico Nacional, 07738, Mexico, CDMX, México

    J. Bory Reyes

  2. Department of Actuarial Sciences, Physics and Mathematics, Universidad de las Américas Puebla, San Andrés Cholula, Puebla, 72810, México

    M. A. Pérez-de la Rosa

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  1. J. Bory Reyes
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  2. M. A. Pérez-de la Rosa
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Correspondence to M. A. Pérez-de la Rosa.

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Bory Reyes, J., Pérez-de la Rosa, M.A. On the Moisil-Theodoresco Operator in Orthogonal Curvilinear Coordinates. Comput. Methods Funct. Theory 21, 131–144 (2021). https://doi.org/10.1007/s40315-020-00319-8

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