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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 1 (January 2023)   > Article

Zak transform for groupoids with abelian isotropy

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


Ibrahima Toure
Université Félix Houphouët-Boigny
Côte d’Ivoire

Kinvi Kangni
Université Félix Houphouët-Boigny
Côte d’Ivoire



Published on 12 January 2023   DOI : 10.21494/ISTE.OP.2023.0904

Abstract

Résumé

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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