Abstract

SANTIESTEBAN, Daniel Alfonso. On some linear operators in Clifford analysis. Rev. Mat [online]. 2024, vol.31, n.2, pp.167-193. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v31i2.56295.

In the late 1970s, the term Clifford Analysis was first used by the American mathematician John Ryan. Several decades have passed and this autonomous discipline in mathematical analysis has proven to be extremely effective in rewriting many of the equations of mathematical physics. In this article we will obtain some interesting results on linear operators that are related to functional spaces that arise specifically in Clifford algebras. The connection of some of these operators with the well-known Lamé-Navier system in Linear Elasticity makes it possible to study essential properties and natural generalizations to high dimensions. At the end, new Dirac operators constructed with arbitrary orthonormal bases of Euclidean space will be considered.

Keywords : Linear operators; Clifford algebras; Dirac operators..

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