The Clifford Deformation of the Hermite Semigroup
  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. 
Hendrik De Bie, Bent Orsted, Petr Somberg and Vladimir Soucek
math.CA math-ph math.MP math.RT