Computational Methods and Function Theory 9 (2009), No. 1, 199--212
Copyright Heldermann Verlag 2009
Richard Delanghe
richard.delanghe@UGent.be , University of Ghent, Department of Mathematical Analysis, Galglaan 2, B-9000 Gent, Belgium.
The space of homogeneous polynomial solutions of degree k of the Moisil-Théodoresco system in R3 is isomorphic to the real vector space MT+(R3; R+0,3;k) of homogeneous R+0,3-valued polynomial null-solutions of degree k of the Cauchy-Riemann operator Dx in R3. Hereby R+0,3 is the even subalgebra of the Clifford algebra R0,3. A structure theorem is proved for the elements Wk ∈ MT+ (R3;R+0,3; k), based essentially on conjugate harmonicity, and a general procedure is elaborated for constructing bases of MT+ (R3; R+0,3;k).
Keywords: Moisil-Théodoresco system, homogeneous monogenic polynomials, harmonic potentials.
MSC 2000: 30G35.
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