@ARTICLE{10.21494/ISTE.OP.2023.0904, 

TITLE={Zak transform for groupoids with abelian isotropy}, 
  
AUTHOR={Ibrahima Toure, Kinvi Kangni, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={14}, 

NUMBER={Issue 1 (January 2023)}, 
	
YEAR={2023}, 

URL={http://www.openscience.fr/Zak-transform-for-groupoids-with-abelian-isotropy}, 
	
DOI={10.21494/ISTE.OP.2023.0904}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={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.}}