Analysis of the quadratic term in the backscattering transformation

Abstract

The quadratic term in the Taylor expansion at the origin of the backscattering transformation in odd dimensions $n\ge 3$ gives rise to a symmetric bilinear operator $B_2$ on $C_0^{\infty }({\mathbb{R}}^n)\times C_0^{\infty }({\mathbb{R}}^n)$. In this paper we prove that $B_2$ extends to certain Sobolev spaces with weights and show that it improves both regularity and decay.

14 pages

Cited by in corpus (1)

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