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arXiv · 1204.2688

Minkowski curvelets and wave equations

Jeremie Unterberger
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Abstract

We define a new type of wavelet frame adapted to the study of wave equations, that we call 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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Jeremie Unterberger. 2012-04-12. Minkowski curvelets and wave equations. https://arxiv.org/abs/1204.2688

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