Embedding Factors for Branching in Hermitian Clifford Analysis

Abstract

A step 2 branching decomposition of spaces of homogeneous Hermitian monogenic polynomials is established with explicit embedding factors in terms of the generalized Jacobi polynomials, which allows for an inductive construction of an orthogonal basis for those spaces. The embedding factors and the orthogonal bases are fully worked out in the complex dimension 2 case, with special interest for the Appell property.

Keywords

• Clifford analysis
• Hermitian monogenic
• Step 2 branching
• Embedding factor