  In this paper, we prove dispersion estimates for the boundary integral
operator associated with the fourth order Schr\"odinger equation posed on the
half line. Proofs of such estimates for domains with boundaries are rare and
generally require highly technical approaches, as opposed to our simple
treatment which is based on constructing a boundary integral operator of
oscillatory nature via the Fokas method. Our method is uniform and can be
extended to other higher order partial differential equations where the main
equation possibly involves more than one spatial derivatives.
