Local Smoothing for the Backscattering Transform

An analysis of the backscattering data for the Schrodinger operator in odd dimensions n3 motivates the introduction of the backscattering transform [image omitted]. This is an entire analytic mapping and we write [image omitted] where BNv is the Nth order term in the power series expansion at v=0. In this paper we study estimates for BNv in H(s) spaces, and prove that Bv is entire analytic in vH(s)E' when s(n-3)/2.