Using Hart Smith’s, curvelet, and shearlet transforms, we investigate L functions with sufficiently smooth background and present here sufficient and necessary conditions, which include the special case with 1-dimensional singularity line. Specifically, we consider the situation where regularity on a line in a non-parallel direction is much lower than directional regularity along the line in a ...

In this paper we show that the shearlets, an affine-like system of functions recently introduced by the authors and their collaborators, are essentially optimal in representing 2–dimensional functions f that are C2 except for discontinuities along C2 curves. More specifically, if fS N is the N–term reconstruction of f obtained by using the N largest coefficients in the shearlet representation, ...

Sobolev wavefront sets and 2-microlocal spaces play a key role in describing analyzing the singularities of distributions microlocal analysis solutions partial differential equations. Employing continuous shearlet transform to spaces, this paper we characterize sets, local Hölder distributions/functions. We then establish connections among through transform.