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We consider a basic $d$-adic model for the scattering transform on the line.We prove $L^2$ bounds for this scattering transform and a weak $L^2$ bound fora Carleson type maximal operator. The latter implies boundedness of $d$-adicmodels of generalized eigenfunctions of Dirac type operators with potential in$L^2(R)$. We show that this result cannot be obtained by estimating the termsin the natural multilinear expansion of the scattering transform.Comment: 31 pages, 2 pictures, submitted, Nonlinearit

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