  We prove a structure formula for the wave operators in R^3 and their adjoints
for a scaling-invariant class of scalar potentials V, under the assumption that
zero is neither an eigenvalue, nor a resonance for -\Delta+V.
  The formula implies the boundedness of wave operators on L^p spaces, 1 \leq p
\leq \infty, on weighted L^p spaces, and on Sobolev spaces, as well as
multilinear estimates for e^{itH} P_c.
  When V decreases rapidly at infinity, we obtain an asymptotic expansion of
the wave operators. The first term of the expansion is of order < y >^{-4},
commutes with the Laplacian, and exists when V \in <x >^{-3/2-\epsilon} L^2.
  We also prove that the scattering operator S = W_-^* W_+ is an integrable
combination of isometries.
  The proof is based on an abstract version of Wiener's theorem, applied in a
new function space.
