Expression for the Number of Eigenvalues of a Friedrichs Model

We consider the self-adjoint operator of a generalized Friedrichs model whose essential spectrum may contain lacunas. We obtain a formula for the number of eigenvalues lying on an arbitrary interval outside the essential spectrum of this operator. We find a sufficient condition for the discrete spectrum to be finite. Applying the formula for the number of eigenvalues, we show that there exist an infinite number of eigenvalues on the lacuna for a particular Friedrichs model and obtain the asymptotics for the number of eigenvalues.