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Anisotropic Meshless Frames on ℝn

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Abstract

We present a construction of anisotropic multiresolution and anisotropic wavelet frames based on multilevel ellipsoid covers (dilations) of ℝn. The wavelets we construct are C ∞ functions, can have any prescribed number of vanishing moments and fast decay with respect to the anisotropic quasi-distance induced by the cover. The dual wavelets are also C ∞, with the same number of vanishing moments, but with only mild decay with respect to the quasi-distance. An alternative construction yields a meshless frame whose elements do not have vanishing moments, but do have fast anisotropic decay.

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Authors and Affiliations

  1. GE Healthcare, 27 Hamaskit St., Herzelia, 46733, Israel

    S. Dekel

  2. Department of Mathematics, Auburn University, Auburn, AL, 36849-5310, USA

    Y. Han

  3. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    P. Petrushev

Authors
  1. S. Dekel
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  2. Y. Han
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  3. P. Petrushev
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Corresponding author

Correspondence to S. Dekel.

Additional information

Communicated by Peter Casazza.

P. Petrushev has been supported by NFS grant DMS-0709046.

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Dekel, S., Han, Y. & Petrushev, P. Anisotropic Meshless Frames on ℝn . J Fourier Anal Appl 15, 634–662 (2009). https://doi.org/10.1007/s00041-009-9070-4

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  • DOI: https://doi.org/10.1007/s00041-009-9070-4

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