Structure of Solutionsof Polynomial Dirac Equationsin Clifford Analysis

In this note, structures of null solutions of the polynomial Dirac operators D , Dk, Dn þPn1j0 bjD j are studied, where D is the Dirac operator in Rm1, , bj 2 C, j 0,..., n 1, D0 I is the identity operator. Explicit decompositions of null solutions of the polynomial Dirac operators in the respectively relevant sub-spaces are obtained which are used to derive their Taylor series expansions. The solutions of inhomogeneous equation pðDÞf g are discussed for a special class of RðmÞ-valued continuous functions g