Total Rarita-Schwinger operators in Clifford analysis |
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| Authors: | David Eelbode Peter Van Lancker |
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| Institution: | 1. Department of Mathematics, University of Antwerp, Campus Middelheim, G-Building, Middelheimlaan 1, 2020, Antwerpen, Belgium
2. Department of Engineering Sciences, University College Ghent (Member of Ghent University Association), Schoonmeersstraat 52, 9000, Ghent, Belgium
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| Abstract: | Rarita-Schwinger operators in Clifford analysis can be realized as first-order differential operators acting on functions f(x, u) taking values in the vector space of homogeneous monogenic polynomials. In this paper, the Scasimir operator for the orthosymplectic Lie superalgebra will be used to construct an invariant operator which acts on the full space of functions in two vector variables and therefore has more invariance properties. Also the fundamental solution for this operator will be constructed. |
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