We investigate the eigengenvalues problem for self-adjoint operators with the singular perturbations. The general results presented here includes weakly as well as strongly singular cases. We illustrate these results on two models which correspond to so-called additive strongly singular perturbations.
Essential spectrum of a limit of self--adjoint operators
$J$-self-adjoint operators with $\mathcal{C}$-symmetries: extension theory approach
On a class of $J$-self-adjoint operators with empty resolvent set
