Abstract
This paper investigates Gabor frame sets in a periodic subset \(\mathbb S\) of \(\mathbb R\). We characterize tight Gabor sets in \(\mathbb S\), and obtain some necessary/sufficient conditions for a measurable subset of \(\mathbb S\) to be a Gabor frame set in \(\mathbb S\). We also characterize those sets \(\mathbb S\) admitting tight Gabor sets, and obtain an explicit construction of a class of tight Gabor sets in such \(\mathbb S\) for the case that the product of time-frequency shift parameters is a rational number. Our results are new even if \(\mathbb S=\mathbb R\).
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Communicated by Qiyu Sun.
Supported by the National Natural Science Foundation of China (Grant No. 10671008, 10901013), Beijing Natural Science Foundation (Grant No. 1092001), the Scientific Research Common Program of Beijing Municipal Commission of Education, the Project-sponsored by SRF for ROCS, SEM of China.
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Lian, QF., Li, YZ. Gabor frame sets for subspaces. Adv Comput Math 34, 391–411 (2011). https://doi.org/10.1007/s10444-010-9161-4
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DOI: https://doi.org/10.1007/s10444-010-9161-4