On the spectrum of convolution operator with a potential

This paper focuses on the spectral properties of a bounded self-adjoint operator in L2(Rd) being sum convolution with an integrable kernel and multiplication by continuous potential converging to zero at infinity. We study both essential discrete spectra this operator. It is shown that spectrum union image potential. then provide number sufficient conditions for existence obtain lower upper bounds eigenvalues. Special attention paid case operators possessing countably many points spectrum. also compare considered work those classical Schrödinger operators.