Title: Averaged wave operators on the singular spectrum.
Abstract: Classical scattering theory establishes the existence of strong wave operators on the absolutely continuous subspace for a pair of selfadjoint operators on a Hilbert space, whose difference belongs to the trace class. On the singular spectrum the analog of this result obviously fails. We deal with a much weaker case, namely, we discuss the averaged convergence in the weak operator topology. Our results are connected with the Hilbert transform with respect to a singular measure on the real line.
