A quaternionic analogue of the Segal-Bargmann transform
Complex Variables
2017-05-10 v2
Abstract
The Bargmann-Fock space of slice hyperholomorphic functions is recently introduced by Alpay, Colombo, Sabadini and Salomon. In this paper, we reconsider this space and present a direct proof of its independence of the slice. We also introduce a quaternionic analogue of the classical Segal-Bargmann transform and discuss some of its basic properties. The explicit expression of its inverse is obtained and the connection to the left one-dimensional quaternionic Fourier transform is given.
Cite
@article{arxiv.1603.05052,
title = {A quaternionic analogue of the Segal-Bargmann transform},
author = {K. Diki and A. Ghanmi},
journal= {arXiv preprint arXiv:1603.05052},
year = {2017}
}