Local smoothing for the backscattering transform

Abstract

An analysis of the backscattering data for the Schrödinger operator in odd dimensions $n\ge 3$ motivates the introduction of the backscattering transform $B:C_0^{\infty }({\mathbb{R}}^n;\mathbb{C})\to C^{\infty }({\mathbb{R}}^n;\mathbb{C})$. This is an entire analytic mapping and we write $Bv={\sum }_1^{\infty }{B}_{N}v$ where $B_{N}v$ is the $N$:th order term in the power series expansion at $v=0$. In this paper we study estimates for $B_{N}v$ in $H_{(s)}$ spaces, and prove that $Bv$ is entire analytic in $v \in H_{(s)}\cap \Cal E'$ when $s\ge (n-3)/2$.

22 pages

Cited by in corpus (1)

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