Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states
Mathematical Physics
2015-06-05 v1 math.MP
Quantum Physics
Abstract
We define quaternionic Hermite polynomials by analogy with two families of complex Hermite polynomials. As in the complex case, these polynomials consatitute orthogonal families of vectors in ambient quaternionic -spaces. Using these polynomials, we then define regular and anti-regular subspaces of these -spaces, the associated reproducing kernels and the ensuing quaternionic coherent states.
Cite
@article{arxiv.1206.3684,
title = {Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states},
author = {K. Thirulogasanthar and S. Twareque Ali},
journal= {arXiv preprint arXiv:1206.3684},
year = {2015}
}