On Plancherel’s Identity for a Two–dimensional Scattering Transform
نویسندگان
چکیده
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 scattering transform was established by Beals–Coifman for Schwartz functions. Sung extended the validity of the identity to functions belonging to L(R) ∩ L∞(R2) and Brown to L(R)–functions with sufficiently small norm. More recently, Perry extended to the weighted Sobolev space H(R) and here we extend to H(R) with s ∈ (0, 1).
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