摘要
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）.
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）.
基金
Supported by National Natural Science Foundation of China(Grant Nos.10901013and11271037)
Beijing Natural Science Foundation(Grant No.1122008)
Fundamental Research Funds for the Central Universities(Grant No.2011JBM299)
