Differential operators with distribution coefficients

The problem of the correct definition of the Schroedinger operator with point interactions was initiated by physicists (L. D. Landau and E. M. Lifshits. Theoretical Physics. Vol. 3). The study of this problem was carried out in the 60-ies by F. A. Berezin, R. A. Minlos and L. D. Faddev. Subsequently there have been numerous works on this subject, in particular, for potentials having supports on hypersurfaces. In the one-dimensional case for the Sturm-Liouville operator, the correct definition was proposed by M. G. Krein, and also by F. Atkinson for the case when antiderivative of a potential (in the sense of distributions) is a function of bounded variation.
About 20 years ago the author proposed a method of regularization and a method of multipliers to work with these operators under more general conditions on the potential. The talk will tell about the development of these methods in the works of the author, his students and colleagues.