The Continuous Shearlet Transform in Arbitrary Space Dimensions

  title={The Continuous Shearlet Transform in Arbitrary Space Dimensions},
  author={Stephan Dahlke and Gabriele Steidl and Gerd Teschke},
  journal={Journal of Fourier Analysis and Applications},
This paper is concerned with the generalization of the continuous shearlet transform to higher dimensions. Similar to the two-dimensional case, our approach is based on translations, anisotropic dilations and specific shear matrices. We show that the associated integral transform again originates from a square-integrable representation of a specific group, the full n-variate shearlet group. Moreover, we verify that by applying the coorbit theory, canonical scales of smoothness spaces and… 
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  • H. Führ, Ren'e Koch
  • Mathematics
    2019 13th International conference on Sampling Theory and Applications (SampTA)
  • 2019
It is shown that different groups lead to different approximation theories, which relies on a rigidity theorem which states that geometrically incompatible coverings leading to different decomposition spaces in almost all cases.


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