广义后向散射与Lax-Phillips变换
Generalized backscattering and the Lax-Phillips transform
摘要：
使用自由空间的平移表示（修改的拉冬变换）的Lax和菲利普斯在奇数维，它表明，广义后向散射变换（因此出射角$ω=Sθ$的入射角与$S$正交和$\Id-S$可逆）可以进一步限制，以给出一个完整的，全球Fredholm，适当的索伯列夫空间的潜力与紧支持的运营商。作为推论，我们表明，修改后的背散射映射是一个局部同构附近的元素的脱殊集的潜力。
英文摘要：
Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle $ω=Sθ$ in terms of the incoming angle with $S$ orthogonal and $\Id-S$ invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact support. As a corollary we show that the modified backscattering map is a local isomorphism near elements of a generic set of potentials.
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