Density of irregular wavelet frames
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- by Wenchang Sun and Xingwei Zhou PDF
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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.References
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Additional Information
- Wenchang Sun
- Affiliation: Department of Mathematics, Nankai University, Tianjin 300071, China
- ORCID: 0000-0002-5841-9950
- Email: sunwch@nankai.edu.cn
- Xingwei Zhou
- Affiliation: Department of Mathematics, Nankai University, Tianjin 300071, China
- Email: xwzhou@nankai.edu.cn
- Received by editor(s): February 3, 2003
- Received by editor(s) in revised form: May 7, 2003
- Published electronically: February 26, 2004
- Additional Notes: This work was supported by the National Natural Science Foundation of China (10171050 and 10201014), the Mathematical Tianyuan Foundation (TY10126007), the Research Fund for the Doctoral Program of Higher Education, and the Liuhui Center for Applied Mathematics.
- Communicated by: David R. Larson
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2377-2387
- MSC (2000): Primary 42C40, 41A58
- DOI: https://doi.org/10.1090/S0002-9939-04-07410-6
- MathSciNet review: 2052416