Complete orthogonal Appell systems for spherical monogenics

Abstract

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.Comment: to appear in Complex Anal. Oper. Theory; a presentation of the main results completely changed and a new section on spherical harmonics adde