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The Clifford Deformation of the Hermite Semigroup
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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The Clifford Deformation of the Hermite Semigroup
Інший ID:
2010 Mathematics Subject Classification: 33C52; 30G35; 43A32
DOI: http://dx.doi.org/10.3842/SIGMA.2013.010
DOI: http://dx.doi.org/10.3842/SIGMA.2013.010
Посилання:
The Clifford Deformation of the Hermite Semigroup / H. De Bie, B. Ørsted, P. Somberg, V. Souček // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 29 назв. — англ.
Підтримка:
H. De Bie would like to thank E. Opdam and J. Stokman for valuable input and discussions during his visit to the Korteweg–de Vries Institute for Mathematics in Amsterdam. This visit was supported by a Postdoctoral Fellowship of the Research Foundation – Flanders (FWO). The last two authors would like to acknowledge support of the research grant GA CR P201/12/G028.
Дата:
2013
Переглядів:
577
Завантажень:
239
Анотація:
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.
