JournalsrmiVol. 28, No. 4pp. 1165–1192

Gelfand–Tsetlin bases for spherical monogenics in dimension 3

  • Sebastian Bock

    Bauhaus-Universität Weimar, Germany
  • Klaus Gürlebeck

    Bauhaus-Universität Weimar, Germany
  • Roman Lávička

    Charles University, Prague, Czech Republic
  • Vladimír Souček

    Charles University, Prague, Czech Republic
Gelfand–Tsetlin bases for spherical  monogenics in dimension 3 cover
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Abstract

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.

Cite this article

Sebastian Bock, Klaus Gürlebeck, Roman Lávička, Vladimír Souček, Gelfand–Tsetlin bases for spherical monogenics in dimension 3. Rev. Mat. Iberoam. 28 (2012), no. 4, pp. 1165–1192

DOI 10.4171/RMI/708