%0 Journal Article
%T The Clifford Deformation of the Hermite Semigroup
%A Hendrik De Bie
%A Bent £¿rsted
%A Petr Somberg
%A Vladimir Sou£¿ek
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2013
%I National Academy of Science of Ukraine
%X This paper is a continuation of the paper [De Bie H.,  rsted B., Somberg P., Sou ek V., Trans. Amer. Math. Soc. 364 (2012), 3875¨C3902], 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 [Ben Sa d S., Kobayashi T.,  rsted B., Compos. Math. 148 (2012), 1265¨C1336]. 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.
%K Dunkl operators
%K Clifford analysis
%K generalized Fourier transform
%K Laguerre polynomials
%K Kelvin transform
%K holomorphic semigroup
%U http://dx.doi.org/10.3842/SIGMA.2013.010