Gabor frame sets for subspaces

Authors:
Qiao-Fang Lian;Yun-Zhang Li
Affiliations:
Department of Mathematics, Beijing Jiaotong University, Beijing, People's Republic of China 100044;College of Applied Sciences, Beijing University of Technology, Beijing, People's Republic of China 100124
Venue:
Advances in Computational Mathematics
Year:
2011

Citing 4
Cited 0

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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 $\mathbb S=\mathbb R$ .