  We study the effect of algebraically localized impurities on striped phases
in one space-dimension. We therefore develop a functional-analytic framework
which allows us to cast the perturbation problem as a regular Fredholm problem
despite the presence of essential spectrum, caused by the soft translational
mode. Our results establish the selection of jumps in wavenumber and phase,
depending on the location of the impurity and the average wavenumber in the
system. We also show that, for select locations, the jump in the wavenumber
vanishes.
