Inversion Formula for Shearlet Transform in Arbitrary Space Dimensions

In this article, we study the convergence of the inverse shearlet transform in arbitrary space dimensions. For every pair of admissible shearlets, we show that although the integral involved in the inversion formula from the continuous shearlet transform is convergent in the L-2 sense, it is not true in general whenever pointwise convergence is considered. We give some sucient conditions for the pointwise convergence to hold. Moreover, for any pair of admissible shearlets we show that the Riemannian sums defined by the inverse shearlet transform are convergent to the original function as the sampling density tends to infinity.