Abstract
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.
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Dedicated to Prof. Rajab Ali Kamyabi Gol on the occasion of his 55th birthday.
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Arefijamaal, A.A. The Continuous Zak Transform and Generalized Gabor Frames. Mediterr. J. Math. 10, 353–365 (2013). https://doi.org/10.1007/s00009-012-0178-4
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DOI: https://doi.org/10.1007/s00009-012-0178-4