The Clifford Deformation of the Hermite Semigroup
Classical Analysis and ODEs
2013-02-06 v2 Mathematical Physics
math.MP
Representation Theory
Abstract
This paper is a continuation of the paper [arXiv:0911.4725], investigating a natural radial deformation of the Fourier transform in the setting of Clifford analysis. At the same time, it gives extensions of many results obtained in [arXiv:0907.3749]. We establish the analogues of Bochner's formula and the Heisenberg uncertainty relation in the framework of the (holomorphic) Hermite semigroup, and also give a detailed analytic treatment of the series expansion of the associated integral transform.
Keywords
Cite
@article{arxiv.1101.5551,
title = {The Clifford Deformation of the Hermite Semigroup},
author = {Hendrik De Bie and Bent Orsted and Petr Somberg and Vladimir Soucek},
journal= {arXiv preprint arXiv:1101.5551},
year = {2013}
}