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- W2024224557 abstract "Density conditions including necessary ones and sufficient ones for irregular wavelet systems to be frames are studied in this paper. We give a definition of affine Beurling density of time-scale parameters and show that for irregular wavelet systems to be Bessel sequences, the time-scale parameters must be relatively uniformly discrete, or equivalently, they must have a finite upper affine Beurling density. We also show that the lower affine Beurling density of time-scale parameters must be positive for a large class of wavelet frames. For sufficient conditions, we prove that for a nice function, every relatively uniformly discrete and (a,b)-dense time-scale sequence will generate a frame if a−1 and b are small enough. Explicit frame bounds are given. We also study the stability of wavelet frames and show that every wavelet frame with arbitrary time-scale parameters is stable provided the generating function is nice enough. Explicit stability bounds are given. Numerical examples show that our results are sharper than some known ones." @default.
- W2024224557 created "2016-06-24" @default.
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- W2024224557 date "2003-09-01" @default.
- W2024224557 modified "2023-09-23" @default.
- W2024224557 title "Density and stability of wavelet frames" @default.
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- W2024224557 doi "https://doi.org/10.1016/s1063-5203(03)00049-6" @default.
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