  We prove (under the condition of A. G. Kushnirenko) that all time changes for
the horocycle flow have purely absolutely continuous spectrum in the
orthocomplement of the constant functions. This provides an answer to a
question of A. Katok and J.-P. Thouvenot on the spectral nature of time changes
for horocycle flows. Our proofs rely on positive commutator methods for
self-adjoint operators.
