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

By Camil Muscalu, Terence Tao, C. Thiele. 2002

53 citations recorded by the source corpus.

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).

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6e7a23296dd6a4c451c383b8cec27e642ba55f84

Citations in the corpus

• A variation norm Carleson theorem (2009, unknown): “The first step in the proof of (48) will be to demonstrate (49) ∫ J∩E ∑ k:ξk−1(x)∈ΩJ |ak(x)|r ′ dx . µr ′ |J |.”