Spherical monogenics on the Lie sphere

AbstractIn this paper, spherical monogenics on the Lie sphere LSm − 1 are introduced, leading to a refinement of the theory of spherical harmonics on LSm − 1 developed by Morimoto. Furthermore, the explicit decomposition in spherical monogenics of the Cauchy-Hua kernel is given and the theory is applied to classes of Spin(m)-invariant operators on Rm and on LSm − 1 itself. Finally, the theory is applied to the spherical means of functions defined on the unit sphere, which satisfy a Spin(m)-invariant Darboux-type system on the Lie sphere