Phase space projections

Abstract: A partition into tiles of the area covered by a convex tree in the Walsh phase plane gives an orthonormal basis for a subspace of L2. There exists a related projection operator, which has been an important tool for dyadic models of the bilinear Hilbert transform. Extending such an approach to the Fourier model is strictly speaking not possible, but satisfactory substitutes can be constructed. This approach was pursued by Muscalu, Tao and Thiele (2002) for proving uniform bounds for multilinear singular integrals with modulation symmetry in dimension one. I discuss a multidimensional variant of the problem. This is based on joint work with Marco Fraccaroli and Christoph Thiele.

mathematical physicsanalysis of PDEsclassical analysis and ODEscombinatoricscomplex variablesfunctional analysisinformation theorymetric geometryoptimization and controlprobability

Audience: researchers in the topic

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