  Consider the resolvent problem associated with the linearized viscous flow
around a rotating body. Within a setting of classical Sobolev spaces, this
problem is not well posed on the whole imaginary axis. Therefore, a framework
of homogeneous Sobolev spaces is introduced where existence of a unique
solution can be guaranteed for every purely imaginary resolvent parameter. For
this purpose, the problem is reduced to an auxiliary problem, which is studied
by means of Fourier analytic tools in a group setting. In the end, uniform
resolvent estimates can be derived, which lead to the existence of solutions to
the associated time-periodic linear problem.
