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The Clifford Deformation of the Hermite Semigroup
Symmetry, integrability and geometry: methods and applications, Tome 9 (2013) Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper is a continuation of the paper [De Bie H., Ørsted B., Somberg P., Souček V., Trans. Amer. Math. Soc. 364 (2012), 3875–3902], 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 Saïd S., Kobayashi T., Ørsted B., Compos. Math. 148 (2012), 1265–1336]. 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: Dunkl operators; Clifford analysis; generalized Fourier transform; Laguerre polynomials; Kelvin transform; holomorphic semigroup. 
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Henrik De Bie; Ben Ørsted; Petr Somberg; Vladimir Souček. The Clifford Deformation of the Hermite Semigroup. Symmetry, integrability and geometry: methods and applications, Tome 9 (2013). http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a9/

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