Embedding Factors for Branching in Hermitian Clifford Analysis

TL;DR

This paper develops an explicit method for constructing orthogonal bases of Hermitian monogenic polynomials in complex spaces, using embedding factors related to Jacobi polynomials, with detailed results in complex dimension 2.

Contribution

It introduces a new branching decomposition with explicit embedding factors, facilitating inductive basis construction in Hermitian Clifford analysis.

Findings

Explicit embedding factors in terms of Jacobi polynomials

Orthogonal bases constructed for complex dimension 2

Analysis of the Appell property in the bases

Abstract

A step 2 branching decomposition of spaces of homogeneous Hermitian monogenic polynomials in C^n 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.