Homogeneous approximation property for continuous shearlet transforms in higher dimensions

Abstract

Abstract This paper is concerned with the generalization of the homogeneous approximation property (HAP) for a continuous shearlet transform to higher dimensions. First, we give a pointwise convergence result on the inverse shearlet transform in higher dimensions. Second, we show that every pair of admissible shearlets possess the HAP in the sense of L 2 ( R d ) $L^{2}(R^{d})$ . Third, we give a sufficient condition for the pointwise HAP to hold, which depends on both shearlets and functions to be reconstructed.

Keywords

• homogeneous approximation property
• continuous shearlet transform
• shearlet
• admissible