On the approximation of functions with line singularities by ridgelets.

In Grohs and Obermeier (2015), the authors discussed the existence of numerically feasible solvers for advection equations that run in optimal computational complexity. In this paper, we complete the last remaining requirement to achieve this goal — by showing that ridgelets, on which the solver is based, approximate functions with line singularities (which may appear as solutions to the advection equation) with the best possible approximation rate (up to arbitrarily small δ>0) if the functions decay sufficiently fast, and with a slight penalty if not.