Zak transform for groupoids with abelian isotropy

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