Moment discretization for ill-posed problems with discrete weakly bounded noise (Q1761417)

The paper studies Tikhonov regularization for compact linear operator equations in Hilbert spaces with discrete data in the form of point evaluations of the right hand side. A noise model called weakly bounded noise is considered, the most important example of which is additive random noise. Under a uniformity assumption on the design order, optimal rates of convergence are shown for classical Hölder source conditions, using a quadrature result for reproducing kernel Hilbert spaces.