The Clifford deformation of the Hermite semigroup

Details The Clifford deformation of the Hermite semigroup The Clifford deformation of the Hermite semigroup

2011-01-28

arxiv.org/abs/1101.5551v1

Mathematics

Classical Analysis and ODEs

27 pages

Scientific paper

This paper is a continuation of the paper [H. De Bie et al., Dunkl operators and a family of realizations of osp(1|2), 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 [S. Ben Said et al., Laguerre semigroup and Dunkl operators, 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.

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