We use Fourier analysis to construct analytically, in the case of a simple geometry, the symbol of a pseudo-differential operator which plays a fundamental role in the solution of the Stokes problem via the Helmholtz formulation. We then use this information to construct a preconditioning operator which appears to be quite efficient, even for complicated geometries, in order to speed up conjugate gradient algorithms for solving the Stokes problem; these properties will be illustrated by results of numerical experiments.