Density results for subspace multiwindow Gabor systems in the rational case |
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Authors: | Qiao Fang Lian Hai Li Ma |
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Institution: | 11115. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, P. R. China
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Abstract: | Let S be a periodic set in R and L2(S) be a subspace of L2 (R). This paper investigates the density problem for multiwindow Gabor systems in L2(S) for the case that the product of time-frequency shift parameters is a rational number. We derive the density conditions for a multiwindow Gabor system to be complete (a frame) in L2(S). Under such conditions, we construct a multiwindow tight Gabor frame for L2(S) with window functions being characteristic functions. We also provide a characterization of a multiwindow Gabor frame to be a Riesz basis for L2(S), and obtain the density condition for a multiwindow Gabor Riesz basis for L2(S). |
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Keywords: | Multiwindow Gabor frames Riesz bases subspaces Zak transform density conditions |
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