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 …

Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally
as sl (2, C)-modules. As finite-dimensional irreducible sl (2, C)-modules, they have …

Hermitian Clifford analysis is a higher dimensional function theory centered around the
simultaneous null solutions, called Hermitian monogenic functions, of two Hermitian …

A complete orthogonal system for the monogenic L 2-space consisting of solid oblate
spheroidal monogenics in 3 is constructed by means of harmonic functions. The lack of …

In this chapter an introduction is given to Clifford analysis and the underlying Clifford
algebras. The functions under consideration are defined on Euclidean space and take …

We prove that the Gram–Schmidt orthogonalization process can be carried out in Hilbert
modules over Clifford algebras, in spite of the un-invertibility and the un-commutativity of …

Abstract Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly
described for homogeneous polynomial solutions of the Hodge-de Rham systems in the …

In this note, we give an explicit description of orthogonal (even the Gelfand-Tsetlin) bases for
the spaces of homogeneous solutions of the Riesz system in R 3 using hypergeometric …

In this paper, we study generating functions for the standard orthogonal bases of spherical
harmonics and spherical monogenics in R^ m R m. Here spherical monogenics are …

This paper gives an overview of some basic results on Hermitian Clifford analysis, a
refinement of classical Clifford analysis dealing with functions in the kernel of two mutually …