English

A Parametrix Construction for the Wave Equation with Low Regularity Coefficients Using a Frame of Gaussians

Analysis of PDEs 2010-03-19 v2

Abstract

We construct a frame of complex Gaussians for the space of L2(Rn)L^2(\mathbb{R}^n) functions. When propagated along bicharacteristics for the wave equation, the frame can be used to build a parametrix with suitable error terms. When the coefficients of the wave equation have more regularity, propagated frame functions become Gaussian beams.

Keywords

Cite

@article{arxiv.1003.2747,
  title  = {A Parametrix Construction for the Wave Equation with Low Regularity Coefficients Using a Frame of Gaussians},
  author = {Alden Waters},
  journal= {arXiv preprint arXiv:1003.2747},
  year   = {2010}
}