On the stability of wavelet and Gabor frames (Riesz bases) |
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Authors: | Zhang Jing |
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Affiliation: | (1) Institute of Mathematics, Academia sinica, Beijing, P. R. of China |
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Abstract: | If the sequence of functions j, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system j,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of or is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16]. |
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Keywords: | 26B05 42B10 42C99 |
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