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Necessity of Oversampling Theorem for Affine Frames

DOI: 10.4236/jamp.2014.22003    2,542 Downloads   3,840 Views  

ABSTRACT

In this paper we prove that n is relatively prime to a which is also necessary.

Cite this paper

Fang, Q. , Shi, X. and Li, W. (2014) Necessity of Oversampling Theorem for Affine Frames. Journal of Applied Mathematics and Physics, 2, 18-23. doi: 10.4236/jamp.2014.22003.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] C. Lee, P. Linneman and C. K. Chui, “An Introduction to Wavelets,” Academic Press, Boston, 1992.
[2] I. Daubechies, “Ten Lectures on Wavelets,” Society for Industrial and Applied Mathematics, Philadelphia, 1992.
http://dx.doi.org/10.1137/1.9781611970104
[3] C. K. Chui and X. L. Shi, “Bessel Sequences and Affine Frames,” Applied and Computational Harmonic Analysis, Vol. 1, No. 1, 1993, pp. 29-49. http://dx.doi.org/10.1006/acha.1993.1003
[4] C. K. Chui and X. L. Shi, n× Oversampling preserves any tight affine frame for odd n, Proceedings of the American Mathematical Society, Vol. 121, No, 2, 1994, pp. 511-517.

  
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