On weighted Dirac operators and their fundamental solutions

Abstract

In this work we dene a Dirac type operator with constants weights which factorizes the Laplace operator in the classic sense. We characterize a family of operators of this type whose weights are elements of a subspace of the Clifford algebra An. For this operator we construct a fundamental solution and get a Cauchy-Pompeiu integral formula.

Key words: Dirac operators, fundamental solutions, Clifford algebras.