Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation operators applied to it, in much the same way wavelet systems are dyadic scalings and translations of a single function, but including a precise control of directio...

In this note, we present results on the representation of any compactly supported distribution by a nite linear combination of linearly independent integer translates of distributions. As an application we obtain a self-adaptive stability lemma.