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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Density of irregular wavelet frames


Authors: Wenchang Sun and Xingwei Zhou
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2377-2387
MSC (2000): Primary 42C40, 41A58
Published electronically: February 26, 2004
MathSciNet review: 2052416
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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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Additional Information

Wenchang Sun
Affiliation: Department of Mathematics, Nankai University, Tianjin 300071, China
Email: sunwch@nankai.edu.cn

Xingwei Zhou
Affiliation: Department of Mathematics, Nankai University, Tianjin 300071, China
Email: xwzhou@nankai.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07410-6
PII: S 0002-9939(04)07410-6
Keywords: Wavelet frames, density, Beurling density
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
Article copyright: © Copyright 2004 American Mathematical Society