IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Anisotropic meshless frames on Rn

A 2009 Preprint by S. Dekel, Y. Han, and P. Petrushev

  • 2009:01
  • We present a construction of anisotropic multiresolution and anisotropic wavelet frames based on multilevel ellipsoid covers (dilations) of R^n. The wavelets we construct are C^{infinity} 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^{infinity}, 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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