Abstract
We show that every rationally sampled dilation-and-modulation system is unitarily equivalent to a multi-window Gabor system with special structures. As a consequence, the study of dilation-and-modulation systems in \(L^2({\mathbb {R}}_+)\) reduces to that of multi-window Gabor systems in \(L^2({\mathbb {R}})\) with special structures.
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The author would like to thank Yun-Zhang Li for interesting discussions.
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Lemvig, J. A Remark on Dilation-and-Modulation Frames for \({L^2({\pmb {\mathbb {R}}_+)}}\). Results Math 75, 110 (2020). https://doi.org/10.1007/s00025-020-01237-w
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DOI: https://doi.org/10.1007/s00025-020-01237-w