Segal-Bargmann-Fock modules of monogenic functions

In this paper, we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extending it to Clifford algebra-valued functions. Then we apply the results to monogenic functions and prove that the Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform for monogenic functionals. This kernel is also the reproducing kernel for the monogenic Bargmann module.In this paper, we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extending it to Clifford algebra-valued functions. Then we apply the results to monogenic functions and prove that the Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform for monogenic functionals. This kernel is also the reproducing kernel for the monogenic Bargmann module.A