  We investigate the effect of spatial inhomogeneity on perfectly periodic,
self-organized striped patterns in spatially extended systems. We demonstrate
that inhomogeneities select a specific translate of the striped patterns and
induce algebraically decaying, dipole-type farfield deformations. Phase shifts
and leading order terms are determined by effective moments of the spatial
inhomogeneity. Farfield decay is proportional to the derivatives of the Green's
function of an effective Laplacian. Technically, we use mode filters and
conjugacies to an effective Laplacian to establish Fredholm properties of the
linearization in Kondratiev spaces. Spatial localization in a contraction
argument is gained through the use of an explicit deformation ansatz and a
subtle cancellation in Bloch wave space.
