Minkowski curvelets and wave equations
Mathematical Physics
2012-10-29 v2 math.MP
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.
Cite
@article{arxiv.1204.2688,
title = {Minkowski curvelets and wave equations},
author = {Jeremie Unterberger},
journal= {arXiv preprint arXiv:1204.2688},
year = {2012}
}
Comments
20 pages, 2 figures - typos corrected