Analysis of the quadratic term in the backscattering transformation

Details Analysis of the quadratic term in the backscattering transformation Analysis of the quadratic term in the backscattering transformation

2008-01-15

arxiv.org/abs/0801.2230v1

Mathematics

Analysis of PDEs

14 pages

Scientific paper

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.

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