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

Dispersion estimates for the boundary integral operator associated with the fourth order Schr\"odinger equation posed on the half line