  We show that formal Schr\"odinger operators with singular potentials from the
space W^{-1}_{2,unif}(R) can be naturally defined to give selfadjoint and
bounded below operators, which depend continuously in the uniform resolvent
sense on the potential in the W^{-1}_{2,unif}(R)-norm. In the case of periodic
singular potentials we also establish pure absolute continuity and a band and
gap structure of the spectrum thus generalising some classical results for
singular potentials of one-dimensional quasicrystal theory.
