A VARIATIONAL APPROACH TO THE INVERSION OF SOME COMPACT OPERATORS

Inverse problems of Fourier synthesis can be regularized by constraining the resolution of the reconstructed object. One may speak of regularization by mollification. This regularization principle has been shown to behave nicely in practice, and more recently to give rise to interesting Tikhonov-like theorems. In this paper, we propose and analyse an extension of the regularization by mollification to a wider class of ill-posed problems.