A Carleson Type Theorem for a Cantor Group Model of the Scattering Transform
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چکیده
We consider a basic d-adic model for the scattering transform on the line. We prove L bounds for this scattering transform and a weak L 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 L(IR). 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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تاریخ انتشار 2003