Recovering discrete and continuous parts of the solution of linear ill-posed problems by Tikhonov regularization

In some applications, e.g. in physical chemistry, linear integral equations of the first kind appear whose solutions consist of continuous parts and discrete parts, i.e., delta-distributions concentrated on certain points. It is of importance to be able to recover both the continuous and the discrete parts. We do this by Tikhonov regularization; note that since also the locations where the discrete parts are concentrated have to be found, the problem is nonlinear.