Zeroes of the spectral density of discrete Schroedinger operator with   Wigner-von Neumann potential
  We consider a discrete Schroedinger operator whose potential is the sum of a Wigner-von Neumann term and a summable term. The essential spectrum of this operator equals to the interval [-2,2]. Inside this interval, there are two critical points where eigenvalues may be situated. We prove that, generically, the spectral density of the operator has zeroes of the power type at these points. 
Sergey Simonov
math.SP