  We carry out the Ewald summation for the Rotne-Prager-Yamakawa mobility
tensor, the Oseen mobility tensor and further variations of both, relevant for
the hydrodynamic interactions in colloidal suspensions, where all interacting
particles are within a single plane, i.e., adsorbed at a fluid interface or
other quasi two-dimensional systems. We use the Poisson summation formula for
systems periodic in two dimensions and finite in the third dimension in order
to obtain simple formulae for applications, such as molecular dynamics or
Brownian dynamics simulations. We show, that for such systems, as soon as noise
is taken into account, a commonly used approximate three-dimensional Ewald
summation leads to a spurious system size dependence, which may considerably
affect the interpretation of simulation results and will be cured within our
approach. Additionally, the resulting formulae are found to be computationally
much less expensive than the approximate three-dimensional Ewald summation.
