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Wavelet sets in ℝn

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Abstract

A congruency theorem is proven for an ordered pair of groups of homeomorphisms of a metric space satisfying an abstract dilation-translation relationship. A corollary is the existence of wavelet sets, and hence of single-function wavelets, for arbitrary expansive matrix dilations on L2(ℝ n). Moreover, for any expansive matrix dilation, it is proven that there are sufficiently many wavelet sets to generate the Borel structure ofℝ n.

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References

  1. Chui, C.K. (1992).An Introduction to Wavelets. Academic Press, New York.

    MATH  Google Scholar 

  2. Daubechies, I. (1992).Ten Lectures on Wavelets. CBMS 61, SIAM.

  3. Dai, X. and Larson, D., Wandering vectors for unitary systems and orthogonal wavelets,Memoirs A.M.S., to appear.

  4. Dai, X. and Lu, S. (1996). Wavelets in subspaces.Mich. J. Math. 43, 81–98.

    Article  MATH  Google Scholar 

  5. Fang, X. and Wang, X. (1996). Construction of minimally-supported-frequencies wavelets.J. Fourier Analysis and Applications. 2, 315–327.

    MATH  Google Scholar 

  6. Hernandez, E., Wang, X., and G. Weiss (1996). Smoothing minimally supported frequency (MSF) wavelets: Part I.J. Fourier Analysis and Applications. 2, 329–340.

    MATH  Google Scholar 

  7. Hernandez, E., Wang, X., and G. Weiss, Smoothing minimally supported frequency (MSF) wavelets: Part II.J. Fourier Analysis and Applications, to appear.

  8. Meyer, Y. (1992).Wavelets and Operators, Cambridge Studies in Advanced Mathematics. 37.

  9. Robinson, C. (1995).Dynamical Systems. CRC Press, Boca Raton, FL.

    MATH  Google Scholar 

  10. Speegle, D., Thes-elementary wavelets are connected, preprint.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Univ. of North Carolina, 28223, Charlotte, NC

    Xingde Dai

  2. Department of Mathematics, Texas A&M University, 77843, College Station, TX

    David R. Larson & Darrin M. Speegle

Authors
  1. Xingde Dai
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  2. David R. Larson
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  3. Darrin M. Speegle
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Additional information

The second author is supported in part by NSF Grant DMS-9401544.

The third author was a Graduate Research Assistant at Workshop in Linear Analysis and Probability, Texas A&M University.

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Dai, X., Larson, D.R. & Speegle, D.M. Wavelet sets in ℝn . The Journal of Fourier Analysis and Applications 3, 451–456 (1997). https://doi.org/10.1007/BF02649106

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  • DOI: https://doi.org/10.1007/BF02649106

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