On Plancherel's identity for a two-dimensional scattering transform
On Plancherel's identity for a two-dimensional scattering transform
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关于二维散射变换的 Plancherel 恒等式
DOI：
10.1088/0951-7715/28/8/2721
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发表时间：
2015
期刊：
影响因子：
1.7
通讯作者：
K. Rogers
中科院分区：
文献类型：
--
作者：
K. Astala;Daniel Faraco;K. Rogers
We consider the -Dirac system that Ablowitz and Fokas used to transform the defocussing Davey–Stewartson system to a linear evolution equation. The nonlinear Plancherel identity for the associated scattering transform was established by Beals and Coifman for Schwartz functions. Sung extended the validity of the identity to functions belonging to and Brown to L2-functions with sufficiently small norm. More recently, Perry extended to the weighted Sobolev space and here we extend to with 0 < s < 1.
