On the Kato-Rosenblum and Weyl-von Neumann Theorems

The validity of the Kato-Rosenblum and Weyl-von Neumann theorems for nonadditive perturbations in the class ExtA of self adjoint extensions of a symmetric operator A in a separable Hilbert space has been reported. It has been stressed that non-additive perturbations naturally arise in the study of elliptic boundary problems in various domains. Its role in the spectral theory is similar to the role of the classical Weyl function in the spectral theory of singular Sturm-Liouville operators. The following result (regularity theorem) is an analogue of the classical result on the regularity (up to the boundary) of solutions to linear elliptic boundary problems with good coefficients and a good boundary.