A Carleson type theorem for a Cantor group model of the scattering transform

Abstract

We consider a basic d-adic model for the scattering transform on the line. We prove L2 bounds for this scattering transform and a weak L2 bound for a Carleson type maximal operator (theorem 1.4). The latter implies boundedness of d-adic models of generalized eigenfunctions of Dirac type operators with potential in L2(). We show that this result cannot be obtained by estimating the terms in the natural multilinear expansion of the scattering transform (proposition 5.1).

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• Nonlinearity - View
• arXiv (Cornell University) - View - PDF
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