Structure of solutions of polynomial Dirac equations in Clifford analysis

Abstract

In this note, structures of null solutions of the polynomial Dirac operators D−λ D^k , are studied, where D is the Dirac operator in is the identity operator. Explicit decompositions of null solutions of the polynomial Dirac operators in the respectively relevant subspaces are obtained which are used to derive their Taylor series expansions. The solutions of inhomogeneous equation p(D)f=g are discussed for a special class of R( ^m )-valued continuous functions g.

Keywords:

• Dirac operator
• Monogenic function
• Polynomial Dirac operator
• MR (2000) AMS Subject Classifications: 30G35