On Plancherel's identity for a two-dimensional scattering transform

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 val...

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Bibliographic Details
Published inNonlinearity Vol. 28; no. 8; pp. 2721 - 2729
Main Authors Astala, Kari, Faraco, Daniel, Rogers, Keith M
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.08.2015
Subjects
Intersections
inverse problem
Linear evolution equations
nonlinear systems
Nonlinearity
Norms
Scattering
scattering transform
Sobolev space
Transforms
Two dimensional
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Summary: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.
Bibliography:London Mathematical Society
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ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/28/8/2721