Revista Matemática Iberoamericana


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Volume 28, Issue 4, 2012, pp. 1165–1192
DOI: 10.4171/RMI/708

Published online: 2012-10-14

Gelfand–Tsetlin bases for spherical monogenics in dimension 3

Sebastian Bock[1], Klaus Gürlebeck[2], Roman Lávička[3] and Vladimír Souček[4]

(1) Bauhaus-Universität Weimar, Germany
(2) Bauhaus-Universität Weimar, Germany
(3) Charles University, Prague, Czech Republic
(4) Charles University, Prague, Czech Republic

The main aim of this paper is to recall the notion of Gelfand–Tsetlin bases (GT bases for short) and to use it for an explicit construction of orthogonal bases for the spaces of spherical monogenics (i.e., homogeneous solutions of the Dirac or the generalized Cauchy–Riemann equation, respectively) in dimension 3. In the paper, using the GT construction, we obtain explicit orthogonal bases for spherical monogenics in dimension 3. We compare them with those constructed by the first and the second author recently (by a direct analytic approach) and we show in addition that the GT basis has the Appell property with respect to all three variables. The last fact is quite important for future applications.

Keywords: Orthogonal basis, Gelfand–Tsetlin basis, Appell property, quaternionic analysis, Clifford analysis

Bock Sebastian, Gürlebeck Klaus, Lávička Roman, Souček Vladimír: Gelfand–Tsetlin bases for spherical monogenics in dimension 3. Rev. Mat. Iberoamericana 28 (2012), 1165-1192. doi: 10.4171/RMI/708