On the spectrum of nonlocal convolution operators with potential

The talk will focus on the spectrum of a self-adjoint convolution operator with an integrable kernel that is perturbed by an essentially bounded real valued potential, The potential tends to zero at infinity. We show that the essential spectrum of such an operator is the union of the spectrum of the convolution operator and of the essential range of the potential. Then we provide several sufficient conditions for the existence of a countable sequence of discrete eigenvalues. For operators having non-connected essential spectrum we give sufficient conditions for the existence of discrete eigenvalues in the corresponding spectral gaps.
This is a joint work with D. Borisov and E. Zhizhina.