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
Дата:2011
Автор: Ghorbel, A.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2011
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

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146800
record_format dspace
spelling 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.
work_keys_str_mv AT ghorbela harmonicanalysisinoneparametermetabeliannilmanifolds
first_indexed 2025-12-07T20:05:16Z
last_indexed 2025-12-07T20:05:16Z
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