  The translational motion of a solid sphere near a deformable fluid interface
is studied in the low Reynolds number regime. In this problem, the fluid flow
driven by the sphere is dynamically coupled the instantaneous conformation of
the interface. Using a two-dimensional Fourier transform technique, we are able
to account for the multiple backflows scattered from the interface. The
mobility tensor is then obtained from the matrix elements of the relevant Green
function. This analysis allows us to express the explicit position and
frequency dependence of the mobility. We recover in the steady limit the result
for a sphere near a perfectly flat interface. At intermediate time scales, the
mobility exhibits an imaginary part, which is a signature of the elastic
response of the interface. In the short time limit, we find the intriguing
feature that the perpendicular mobility may, under some circumstances, become
lower than the bulk value. All those results can be explained from the
definition of the relaxation time of the soft interface.
