Non-relativistic quantum particles bounded to an infinite curve in the plane by
the attractive contact delta-interaction are considered. The interval between
the energy of the transversal bound state and zero is shown to belong
to the absolutely continuous spectrum, with possible embedded eigenvalues.
The curve is assumed smooth and non-intersecting, asymptotically
approaching two different half-lines. The proof is inspired by the proof
of Agmon-Kato-Kuroda theorem.