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Refinable Function-Based Construction of Weak (Quasi-)Affine Bi-Frames

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Abstract

Refinable function-based affine frames and affine bi-frames have been extensively studied in the literature. All these works are based on some restrictions on refinable functions. This paper addresses what are expected from two general refinable functions. We introduce the notion of weak (quasi-) affine bi-frame; present a refinable function-based construction of weak (quasi-) affine bi-frames; and obtain a fast algorithm associated with weak affine bi-frames. An example is also given to show that our construction is optimal in some sense.

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Acknowledgments

The authors would like to thank the referees for carefully reviewing this manuscript and for providing valuable comments, which greatly improve its quality. Supported by the National Natural Science Foundation of China (Grant No. 11271037) and Beijing Natural Science Foundation (Grant No. 1122008).

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Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, Beijing , 100124, People’s Republic of China

    Hui-Fang Jia & Yun-Zhang Li

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  1. Hui-Fang Jia
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  2. Yun-Zhang Li
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Correspondence to Yun-Zhang Li.

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Communicated by Stephan Dahlke.

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Jia, HF., Li, YZ. Refinable Function-Based Construction of Weak (Quasi-)Affine Bi-Frames. J Fourier Anal Appl 20, 1145–1170 (2014). https://doi.org/10.1007/s00041-014-9349-y

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  • DOI: https://doi.org/10.1007/s00041-014-9349-y

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