1204.2688 (Jeremie Unterberger)

Minkowski curvelets and wave equations    [PDF]

Jeremie Unterberger

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.

View original: http://arxiv.org/abs/1204.2688