Continuous Shearlet Frames and Resolution of the Wavefront Set

In recent years directional multiscale transformations like the curveletor shearlet transformation have gained considerable attention. The reason for this is that these transforms are unlike more traditional transforms like wavelets able to efficiently handle data with features along edges. The main result confirming this property for shearlets is contained in [21] where it is shown that for very special functions ψ with frequency support in a compact conical wegde the decay rate of the shearlet coefficients of a tempered distribution f with respect to the shearlet ψ can resolve the Wavefront Set of f . We show an analogous result where the only requirement we impose on ψ is essentially to possess sufficiently many anisotropic vanishing moments. We also show how to build frames for L(R) from any such function.