On the approximation of functions with line singularities by ridgelets

Structurally, the proof resembles Candès (2001), where a similar result was proved for a different ridgelet construction, which is however not well-suited for use in a PDE solver (and in particular, not suitable for the CDD-schemes (Cohen et al., 2001) we are interested in). Due to the differences between the two ridgelet constructions, we have to deal with quite a different set of issues, but are also able to relax the (support) conditions on the function being approximated. Finally, the proof employs a new convolution-type estimate that could be of independent interest due to its sharpness.