2011/06/15 by Roman Lávička, Lavicka, R.
Mathematics · Physics and Astronomy · #30G35 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1106.2970
openalex publication_date 2011/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate properties of Gelfand-Tsetlin bases mainly for spherical monogenics, that is, for spinor valued or Clifford algebra valued homogeneous solutions of the Dirac equation in the Euclidean space. Recently it has been observed that in dimension 3 these bases form an Appell system. We show that Gelfand-Tsetlin bases of spherical monogenics form complete orthogonal Appell systems in any dimension. Moreover, we study the corresponding Taylor series expansions for monogenic functions. We obtain analogous results for spherical harmonics as well.