Mediterranean Journal of Mathematics

, Volume 10, Issue 1, pp 353–365 | Cite as

The Continuous Zak Transform and Generalized Gabor Frames

  • Ali Akbar Arefijamaal


Let G be a locally compact abelian group and H be a closed (not necessarily discrete) subgroup of G. In this article, we introduce the notion of Zak transform associated to H and obtain a necessary and sufficient condition to generate continuous Gabor frames for L 2(G). These results can be extended to non-abelian locally compact groups which are semidirect products. As an application, we obtain a characterization of admissible vectors for the regular and quasi regular representations.

Mathematics Subject Classification (2010)

Primary 43A32 Secondary 43A70 


LCA groups Fourier transform Zak transform continuous frame regular representation semidirect product groups 


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© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Computer SciencesSabzevar Tarbiat Moallem UniversitySabzevarIran

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