2012/04/12 by Jérémie Unterberger, Unterberger, Jeremie
Engineering · Mathematics · #35L10 #35Q75 #42B20 #42B37 #42C40 #81T08 #Advanced Mathematical Physics Problems #Advanced Numerical Analysis Techniques #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1204.2688
openalex publication_date 2012/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Candès, 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.