Harmonic Analysis in One-Parameter Metabelian Nilmanifolds
Let G be a connected, simply connected one-parameter metabelian nilpotent Lie group, that means, the corresponding Lie algebra has a one-codimensional abelian subalgebra. In this article we show that G contains a discrete cocompact subgroup. Given a discrete cocompact subgroup Γ of G, we define the...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2011 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146800 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Harmonic Analysis in One-Parameter Metabelian Nilmanifolds / A. Ghorbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. |
Репозитарії
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nasplib_isofts_kiev_ua-123456789-146800 |
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Ghorbel, A. 2019-02-11T15:25:19Z 2019-02-11T15:25:19Z 2011 Harmonic Analysis in One-Parameter Metabelian Nilmanifolds / A. Ghorbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. 1815-0659 https://nasplib.isofts.kiev.ua/handle/123456789/146800 Let G be a connected, simply connected one-parameter metabelian nilpotent Lie group, that means, the corresponding Lie algebra has a one-codimensional abelian subalgebra. In this article we show that G contains a discrete cocompact subgroup. Given a discrete cocompact subgroup Γ of G, we define the quasi-regular representation τ=indΓG1 of G. The basic problem considered in this paper concerns the decomposition of τ into irreducibles. We give an orbital description of the spectrum, the multiplicity function and we construct an explicit intertwining operator between τ and its desintegration without considering multiplicities. Finally, unlike the Moore inductive algorithm for multiplicities on nilmanifolds, we carry out here a direct computation to get the multiplicity formula. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Harmonic Analysis in One-Parameter Metabelian Nilmanifolds Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Harmonic Analysis in One-Parameter Metabelian Nilmanifolds |
| spellingShingle |
Harmonic Analysis in One-Parameter Metabelian Nilmanifolds Ghorbel, A. |
| title_short |
Harmonic Analysis in One-Parameter Metabelian Nilmanifolds |
| title_full |
Harmonic Analysis in One-Parameter Metabelian Nilmanifolds |
| title_fullStr |
Harmonic Analysis in One-Parameter Metabelian Nilmanifolds |
| title_full_unstemmed |
Harmonic Analysis in One-Parameter Metabelian Nilmanifolds |
| title_sort |
harmonic analysis in one-parameter metabelian nilmanifolds |
| author |
Ghorbel, A. |
| author_facet |
Ghorbel, A. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Let G be a connected, simply connected one-parameter metabelian nilpotent Lie group, that means, the corresponding Lie algebra has a one-codimensional abelian subalgebra. In this article we show that G contains a discrete cocompact subgroup. Given a discrete cocompact subgroup Γ of G, we define the quasi-regular representation τ=indΓG1 of G. The basic problem considered in this paper concerns the decomposition of τ into irreducibles. We give an orbital description of the spectrum, the multiplicity function and we construct an explicit intertwining operator between τ and its desintegration without considering multiplicities. Finally, unlike the Moore inductive algorithm for multiplicities on nilmanifolds, we carry out here a direct computation to get the multiplicity formula.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146800 |
| citation_txt |
Harmonic Analysis in One-Parameter Metabelian Nilmanifolds / A. Ghorbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. |
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2025-12-07T20:05:16Z |
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2025-12-07T20:05:16Z |
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