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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| Дата: | 2013 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149198 |
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dspace |
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irk-123456789-1491982019-02-20T01:28:25Z The Clifford Deformation of the Hermite Semigroup De Bie, H. Ørsted, B. Somberg, P. Souček, V. 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. 2013 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149198 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
De Bie, H. Ørsted, B. Somberg, P. Souček, V. |
| spellingShingle |
De Bie, H. Ørsted, B. Somberg, P. Souček, V. The Clifford Deformation of the Hermite Semigroup Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
De Bie, H. Ørsted, B. Somberg, P. Souček, V. |
| author_sort |
De Bie, H. |
| title |
The Clifford Deformation of the Hermite Semigroup |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.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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Symmetry, Integrability and Geometry: Methods and Applications |
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