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We consider the Schroedinger operator L_{\alpha} on the half-line with aperiodic background potential and the Wigner-von Neumann potential of Coulombtype: csin(2\omega x+d)/(x+1). It is known that the continuous spectrum of theoperator L_{\alpha} has the same band-gap structure as the free periodicoperator, whereas in each band of the absolutely continuous spectrum thereexist two points (so-called critical or resonance) where the operatorL_{\alpha} has a subordinate solution, which can be either an eigenvalue or a`half-bound' state. The phenomenon of an embedded eigenvalue is unstable underthe change of the boundary condition as well as under the local change of thepotential, in other words, it is not generic. We prove that in the general casethe spectral density of the operator L_{\alpha} has power-like zeroes atcritical points (i.e., the absolutely continuous spectrum has pseudogaps). Thisphenomenon is stable in the above-mentioned sense.

Zeroes of the spectral density of the periodic Schroedinger operator with Wigner-von Neumann potential