Minkowski curvelets and wave equations

Details Minkowski curvelets and wave equations Minkowski curvelets and wave equations

2012-04-12

arxiv.org/abs/1204.2688v1

Physics

Mathematical Physics

20 pages, 2 figures

Scientific paper

We define a new type of wavelet frame adapted to the study of wave equations, that we call {\em Minkowski curvelets}, by reference to the curvelets introduced by Cand\`es, Demanet and Donoho. These space-time, strongly anisotropic, directional wavelets have a Fourier support which does not intersect the light-cone; their maximal size is proportional to the inverse of the distance to the light-cone. We show that the matrix of the Green kernel of the Klein-Gordon operator on Minkowski space-time has a nearly exponential off-diagonal decay in this basis.

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