Density of irregular wavelet frames |
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Authors: | Wenchang Sun Xingwei Zhou |
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Institution: | Department of Mathematics, Nankai University, Tianjin 300071, China ; Department of Mathematics, Nankai University, Tianjin 300071, China |
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Abstract: | We show that if an irregular multi-generated wavelet system forms a frame, then both the time parameters and the logarithms of scale parameters have finite upper Beurling densities, or equivalently, both are relatively uniformly discrete. Moreover, if generating functions are admissible, then the logarithms of scale parameters possess a positive lower Beurling density. However, the lower Beurling density of the time parameters may be zero. Additionally, we prove that there are no frames generated by dilations of a finite number of admissible functions. |
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Keywords: | Wavelet frames density Beurling density |
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