A Fourier–Borel transform for monogenic functionals

Abstract

We discuss the Fourier–Borel transform for the dual of spaces of monogenic functions. This transform may be seen as a restriction of the classical Fourier–Borel transform for holomorphic functionals, and it transforms spaces of monogenic functionals into quotients of spaces of entire holomorphic functions of exponential type. We prove that, for the Lie ball, these quotient spaces are isomorphic to spaces of monogenic functions of exponential type.