The quadratic contribution to the backscattering transform in the rotation invariant case

Abstract

Considerations of the backscattering data for the Schrödinger operator$H_v= -\Delta+ v$ in $\RR^n$, where $n\ge 3$ is odd, give rise to an entire analytic mapping from $C_0^\infty ( \RRn)$ to $C^\infty (\RRn)$, the backscattering transformation. The aim of this paper is to give formulas for $B_2(v, w)$ where $B_2$ isthe symmetric bilinear operator that corresponds to the quadratic part of the backscattering transformation and $v$ and $w$ are rotation invariant.