The Clifford Deformation of the Hermite Semigroup
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 obtai...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2013 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149198 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
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nasplib_isofts_kiev_ua-123456789-149198 |
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De Bie, H. Ørsted, B. Somberg, P. Souček, V. 2019-02-19T18:30:12Z 2019-02-19T18:30:12Z 2013 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. 1815-0659 2010 Mathematics Subject Classification: 33C52; 30G35; 43A32 DOI: http://dx.doi.org/10.3842/SIGMA.2013.010 https://nasplib.isofts.kiev.ua/handle/123456789/149198 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Clifford Deformation of the Hermite Semigroup Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The Clifford Deformation of the Hermite Semigroup |
| spellingShingle |
The Clifford Deformation of the Hermite Semigroup De Bie, H. Ørsted, B. Somberg, P. Souček, V. |
| title_short |
The Clifford Deformation of the Hermite Semigroup |
| title_full |
The Clifford Deformation of the Hermite Semigroup |
| title_fullStr |
The Clifford Deformation of the Hermite Semigroup |
| title_full_unstemmed |
The Clifford Deformation of the Hermite Semigroup |
| title_sort |
clifford deformation of the hermite semigroup |
| author |
De Bie, H. Ørsted, B. Somberg, P. Souček, V. |
| author_facet |
De Bie, H. Ørsted, B. Somberg, P. Souček, V. |
| publishDate |
2013 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149198 |
| citation_txt |
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. |
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