The nonexistence of shearlet scaling functions (Q654445)

The author proves a number of results showing that there are restrictions on desirable properties like smoothness or speed of decay of scaling functions in a multiresolution analysis associated with a shearlet system in the plane and that the situation thus differs from the one with standard wavelets. These results are established both for traditional shearlet systems and so-called cone-adapted shearlets (where the cones are in the frequency domain).