  The main purpose of this work is the construction of an analytic functional
calculus for Clifford operators, which are operators acting on certain modules
over Clifford algebras. Unlike in some preceding works by other authors, we use
a spectrum defined in the complex plane, and certain stem functions, analytic
in neighborhoods of such a spectrum. The replacement of the slice regular
functions, having values in a Clifford algebra, by analytic stem functions
becomes possible because of an isomorphism induced by a Cauchy type transform,
whose existence is proved in the first part of this work.
