The Clifford Deformation of the Hermite Semigroup

Autor: Hendrik De Bie, Bent Ørsted, Petr Somberg, Vladimir Souček
Jazyk: angličtina
Rok vydání: 2013
Předmět:
Zdroj: Symmetry, Integrability and Geometry: Methods and Applications, Vol 9, p 010 (2013)
Druh dokumentu: article
ISSN: 1815-0659
DOI: 10.3842/SIGMA.2013.010
Popis: 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.
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