Segal-Bargmann-Fock modules of monogenic functions
Complex Variables
2017-11-06 v2
Abstract
In this paper we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extend 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.
Keywords
Cite
@article{arxiv.1608.06790,
title = {Segal-Bargmann-Fock modules of monogenic functions},
author = {Dixan Peña Peña and Irene Sabadini and Franciscus Sommen},
journal= {arXiv preprint arXiv:1608.06790},
year = {2017}
}
Comments
11 pages