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Mathématiques   > Accueil   > Avancées en Mathématiques Pures et Appliquées   > Numéro 1 (Janvier 2023)   > Article

Transformée de Zack pour les groupoides à groupe d’isotropie abélien

Zak transform for groupoids with abelian isotropy


Ibrahima Toure
Université Félix Houphouët-Boigny
Côte d’Ivoire

Kinvi Kangni
Université Félix Houphouët-Boigny
Côte d’Ivoire



Publié le 12 janvier 2023   DOI : 10.21494/ISTE.OP.2023.0904

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Abstract

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Let 𝒢 be a second countable locally compact Hausdorff groupoid with abelian isotropy groups and 𝓛 be a lattice bundle in the isotropy subgroupoid 𝒢 ’ of 𝒢. In this paper, we define a Zak transform on 𝒢 relatively to 𝓛 and study some of its properties. Moreover, we use Zak transform to obtain some characterizations of the cyclic subbundle of the left regular representation of 𝒢 restricted to 𝓛.

Let 𝒢 be a second countable locally compact Hausdorff groupoid with abelian isotropy groups and 𝓛 be a lattice bundle in the isotropy subgroupoid 𝒢 ’ of 𝒢. In this paper, we define a Zak transform on 𝒢 relatively to 𝓛 and study some of its properties. Moreover, we use Zak transform to obtain some characterizations of the cyclic subbundle of the left regular representation of 𝒢 restricted to 𝓛.

Zak Transform Locally compact groupoids Unitary representations Cyclic subbundles

Zak Transform Locally compact groupoids Unitary representations Cyclic subbundles